Part I, where I go over the official Church teaching.
Part II, where I go over the Biblical evidence.
Part III: The Papacy: A Look at the Biblical Case and the Apostolic Tradition of St. Peter, Vicar of Christ.
So, now we’ll the going through the Church Fathers and seeing what they had to say about the papacy. For this section, I will merely be posting the quotes with as little commentary as possible. These will only be those Church Fathers who wrote and were alive before the First Council of Nicea. These Church Fathers are part of a group called the ante-Nicean Fathers. Since many of my non-Catholic brethren believe that many of the “heresies” of the Catholic Church entered around the time of the First Council of Nicea, when Emperor Constantine enacted the Edict of Milan, I will simply restrict my search to those texts written before such a date.
“You will write therefore two books, and you will send the one to [Pope] Clement and the other to Grapte. And [Pope] Clement will send his to foreign countries, for permission has been granted to him to do so.” Hermas, the Shepherd I:2:4, 80 AD. 
This is considered to be a sign of papal authority because it is the Bishop of Rome, who ultimately, has authority over what the Church may read.
“Our apostles also knew, through our Lord Jesus Christ, that there would be strife on account of the office of the episcopate. For this reason, therefore, inasmuch as they had obtained a perfect fore-knowledge of this, they appointed those [ministers] already mentioned, and afterwards gave instructions, that when these should fall asleep, other approved men should succeed them in their ministry.” St. Clement of Rome, The First Epistle of Clement to the Corinthians 44, 80-95 AD. 
While this does not mention the papacy directly, it does tell us that all of the apostles created successors and that this was entirely in their power to do.
“Ignatius … to the Church … which also presides in the place of the region of the Romans, worthy of God, worthy of honour, worthy of the highest happiness, worthy of praise, worthy of obtaining her every desire, worthy of being deemed holy, and which presides over love, is named from Christ, and from the Father,” St. Ignatius of Antioch, Epistle to the Romans Greeting, 105-110 AD. 
“You have never envied any one; you have taught others. Now I desire that those things may be confirmed [by your conduct], which in your instructions you enjoin [on others].” St. Ignatius of Antioch, Epistle to the Romans 3, 105-110 AD. 
“I do not, as Peter and Paul, issue commandments unto you.” St. Ignatius of Antioch, Epistle to the Romans 4, 105-110 AD. 
This is the earliest statement about the papacy finding their root in Sts. Peter and Paul. Though, the apostolic lineage passes from St. Peter.
“For [Christ] called one of His disciples—previously known by the name of Simon—Peter; since he recognised Him to be Christ the Son of God, by the revelation of His Father: and since we find it recorded in the memoirs of His apostles that He is the Son of God.” St. Justin Martyr, Dialogue of Justin with Trypho 100, 100-165 AD. 
“You have thus by such an admonition bound together the planting of Peter and of Paul at Rome and Corinth. For both of them planted and likewise taught us in our Corinth. And they taught together in like manner in Italy, and suffered martyrdom at the same time.” Dionysius of Corinth, Letter to Pope Soter, 170 AD quoted by Eusebius of Caesarea, Church History II:25:8, 340 AD. 
“For from the beginning it has been your practice to do good to all the brethren in various ways, and to send contributions to many churches in every city. Thus relieving the want of the needy, and making provision for the brethren in the mines by the gifts which you have sent from the beginning, you Romans keep up the hereditary customs of the Romans, which your blessed bishop Soter has not only maintained, but also added to, furnishing an abundance of supplies to the saints, and encouraging the brethren from abroad with blessed words, as a loving father his children.” Dionysius of Corinth, Letter to Pope Soter, 170 AD quoted by Eusebius of Caesarea, Church History IV:23:10, 340 AD. 
“Today we have passed the Lord’s holy day, in which we have read your [Pope Soter] epistle. From it, whenever we read it, we shall always be able to draw advice, as also from the former epistle, which was written to us through Clement.” Dionysius of Corinth, Letter to Pope Soter, 170 AD quoted by Eusebius of Caesarea, Church History IV:23:11, 340 AD. 
This is important, because St. Dionysius of Corinth mentions that they (the Church in Corinth) read the letter of St. Pope Soter to them and also the letter of St. Pope Clement. This means that the bishops of Corinth considered these letters to be inspired, on the level with what we now call sacred scripture, and read them during the liturgy.
“From among these also arose Marcellina, who came to Rome under [the episcopate of] Anicetus, and, holding these doctrines, she led multitudes astray.” St. Irenaeus of Lyons, Irenaeus Against Heresies I:25:6, 175-185 AD. 
I add these kinds of quotes only for the fact that they list the bishops of Rome.
“Cerdo was one who took his system from the followers of Simon, and came to live at Rome in the time of Hyginus, who held the ninth place in the episcopal succession from the apostles downwards.” St. Irenaeus of Lyons, Irenaeus Against Heresies I:27:1, 175-185 AD. 
“Matthew also issued a written Gospel among the Hebrews in their own dialect, while Peter and Paul were preaching at Rome, and laying the foundations of the Church. After their departure, Mark, the disciple and interpreter of Peter, did also hand down to us in writing what had been preached by Peter.” St. Irenaeus of Lyons, Irenaeus Against Heresies III:1:1, 175-185 AD. 
“It is within the power of all, therefore, in every Church, who may wish to see the truth, to contemplate clearly the tradition of the apostles manifested throughout the whole world; and we are in a position to reckon up those who were by the apostles instituted bishops in the Churches, and [to demonstrate] the succession of these men to our own times; those who neither taught nor knew of anything like what these [heretics] rave about. For if the apostles had known hidden mysteries, which they were in the habit of imparting to the perfect apart and privily from the rest, they would have delivered them especially to those to whom they were also committing the Churches themselves. For they were desirous that these men should be very perfect and blameless in all things, whom also they were leaving behind as their successors, delivering up their own place of government to these men; which men, if they discharged their functions honestly, would be a great boon [to the Church], but if they should fall away, the direst calamity.” St. Irenaeus of Lyons, Irenaeus Against Heresies III:3:1, 175-185 AD 
“Since, however, it would be very tedious, in such a volume as this, to reckon up the successions of all the Churches, we do put to confusion all those who, in whatever manner, whether by an evil self-pleasing, by vainglory, or by blindness and perverse opinion, assemble in unauthorized meetings; [we do this, I say,] by indicating that tradition derived from the apostles, of the very great, the very ancient, and universally known Church founded and organized at Rome by the two most glorious apostles, Peter and Paul; as also [by pointing out] the faith preached to men, which comes down to our time by means of the successions of the bishops. For it is a matter of necessity that every Church should agree with this Church, on account of its preeminent authority, that is, the faithful everywhere, inasmuch as the tradition has been preserved continuously by those [faithful men] who exist everywhere.” St. Irenaeus of Lyons, Irenaeus Against Heresies III:3:2, 175-185 AD 
“The blessed apostles, then, having founded and built up the Church, committed into the hands of Linus the office of the episcopate. Of this Linus, Paul makes mention in the Epistles to Timothy. To him succeeded Anacletus; and after him, in the third place from the apostles, Clement was allotted the bishopric. This man, as he had seen the blessed apostles, and had been conversant with them, might be said to have the preaching of the apostles still echoing [in his ears], and their traditions before his eyes. Nor was he alone [in this], for there were many still remaining who had received instructions from the apostles. In the time of this Clement, no small dissension having occurred among the brethren at Corinth, the Church in Rome dispatched a most powerful letter to the Corinthians… To this Clement there succeeded Evaristus. Alexander followed Evaristus; then, sixth from the apostles, Sixtus was appointed; after him, Telephorus, who was gloriously martyred; then Hyginus; after him, Pius; then after him, Anicetus. Soter having succeeded Anicetus, Eleutherius does now, in the twelfth place from the apostles, hold the inheritance of the episcopate. In this order, and by this succession, the ecclesiastical tradition from the apostles, and the preaching of the truth, have come down to us. And this is most abundant proof that there is one and the same vivifying faith, which has been preserved in the Church from the apostles until now, and handed down in truth.” St. Irenaeus of Lyons, Irenaeus Against Heresies III:3:3, 175-185 AD. 
“For Valentinus came to Rome in the time of Hyginus, flourished under Pius, and remained until Anicetus. Cerdon, too, Marcion’s predecessor, himself arrived in the time of Hyginus, who was the ninth bishop. Coming frequently into the Church, and making public confession, he thus remained, one time teaching in secret, and then again making public confession; but at last, having been denounced for corrupt teaching, he was excommunicated from the assembly of the brethren. Marcion, then, succeeding him, flourished under Anicetus, who held the tenth place of the episcopate.” St. Irenaeus of Lyons, Irenaeus Against Heresies III:4:3, 175-185 AD. 
“For why did the Lord send the twelve apostles to the lost sheep of the house of Israel (Matthew 10:6), if these men did not know the truth? How also did the seventy preach, unless they had themselves previously known the truth of what was preached? Or how could Peter have been in ignorance, to whom the Lord gave testimony, that flesh and blood had not revealed to him, but the Father, who is in heaven?” St. Irenaeus of Lyons, Irenaeus Against Heresies III:13:2,175-185 AD. 
“The Lord Himself, too, makes it evident who it was that suffered; for when He asked the disciples, Who do men say that I, the Son of man, am? …and when Peter had replied, You are the Christ, the Son of the living God; and when he had been commended by Him [in these words], That flesh and blood had not revealed it to him, but the Father who is in heaven, He made it clear that He, the Son of man, is Christ the Son of the living God. For from that time forth, it is said, He began to show to His disciples, how that He must go unto Jerusalem, and suffer many things of the priests, and be rejected, and crucified, and rise again the third day… He who was acknowledged by Peter as Christ, who pronounced him blessed because the Father had revealed the Son of the living God to him, said that He must Himself suffer many things, and be crucified; and then He rebuked Peter, who imagined that He was the Christ as the generality of men supposed.” St. Irenaeus of Lyons, Irenaeus Against Heresies III:18:4, 175-185 AD. 
“For the apostles, since they are of more ancient date than all these [heretics], agree with this aforesaid translation; and the translation harmonizes with the tradition of the apostles. For Peter, and John, and Matthew, and Paul, and the rest successively, as well as their followers, did set forth all prophetical [announcements], just as the interpretation of the elders contains them.” St. Irenaeus of Lyons, Irenaeus Against Heresies III:21:3, 175-185 AD. 
“And the presbyters preceding Soter in the government of the Church which you now rule— I mean, Anicetus and Pius, Hyginus and Telesphorus, and Sixtus— did neither themselves observe it [after that fashion], nor permit those with them to do so. Notwithstanding this, those who did not keep [the feast in this way] were peacefully disposed towards those who came to them from other dioceses in which it was [so] observed although such observance was [felt] in more decided contrariety [as presented] to those who did not fall in with it; and none were ever cast out [of the Church] for this matter. On the contrary, those presbyters who preceded you, and who did not observe [this custom], sent the Eucharist to those of other dioceses who did observe it. And when the blessed Polycarp was sojourning in Rome in the time of Anicetus, although a slight controversy had arisen among them as to certain other points, they were at once well inclined towards each other [with regard to the matter in hand], not willing that any quarrel should arise between them upon this head. For neither could Anicetus persuade Polycarp to forego the observance [in his own way], inasmuch as these things had been always [so] observed by John the disciple of our Lord, and by other apostles with whom he had been conversant; nor, on the other hand, could Polycarp succeed in persuading Anicetus to keep [the observance in his way], for he maintained that he was bound to adhere to the usage of the presbyters who preceded him. And in this state of affairs they held fellowship with each other; and Anicetus conceded to Polycarp in the Church the celebration of the Eucharist.” St. Irenaeus of Lyons, Fragments from the Lost Writings of Irenaeus 1:3. 
“Therefore on hearing those words, the blessed Peter, the chosen, the pre-eminent, the first of the disciples, for whom alone and Himself the Saviour paid tribute.” St. Clement of Alexandria, Clemens Alexandrinus on the Salvation of the Rich Man XXI, 182-202 AD. 
“Marcus, my son, salutes you. Mark, the follower of Peter, while Peter publicly preached the Gospel at Rome before some of Cæsar’s equites, and adduced many testimonies to Christ, in order that thereby they might be able to commit to memory what was spoken, of what was spoken by Peter, wrote entirely what is called the Gospel according to Mark.” St. Clement of Alexandria, Fragments I:I, 182-202 AD. 
“And such a ray of godliness shone forth on the minds of Peter’s hearers, that they were not satisfied with the once hearing .. but with all manner of entreaties importuned Mark, to whom the Gospel is ascribed, he being the companion of Peter, that he would leave in writing a record of the teaching which had been delivered to them verbally; and did not let the man alone till they prevailed upon him; and so to them we owe the Scripture called the Gospel by Mark… the apostle [Peter] was delighted with the enthusiasm of the men, and sanctioned the composition for reading in the Churches.” St. Clement of Alexandria, Fragments IV:VII, 182-202 AD. 
“By a similar usage Babylon also in our (St.) John is a figure of the city of Rome, as being like (Babylon) great and proud in royal power, and warring down the saints of God.” Tertullian, Against Marcion III:13, 197-220 AD.  Also in Tertullian, An Answer to the Jews 9, 197-220 AD. 
“On the whole, then, if that is evidently more true which is earlier, if that is earlier which is from the very beginning, if that is from the beginning which has the apostles for its authors, then it will certainly be quite as evident, that that comes down from the apostles, which has been kept as a sacred deposit in the churches of the apostles. Let us see … what utterance also the Romans give, so very near (to the apostles), to whom Peter and Paul conjointly bequeathed the gospel even sealed with their own blood.” Tertullian, Against Marcion IV:5, 197-220 AD. 
“Again, He changes the name of Simon to Peter, inasmuch as the Creator also altered the names of Abram, and Sarai, and Oshea, by calling the latter Joshua, and adding a syllable to each of the former. But why Peter? If it was because of the vigour of his faith, there were many solid materials which might lend a name from their strength. Was it because Christ was both a rock and a stone? For we read of His being placed for a stone of stumbling and for a rock of offense. I omit the rest of the passage. Therefore He would fain impart to the dearest of His disciples a name which was suggested by one of His own special designations in figure.” Tertullian, Against Marcion IV:13, 197-220 AD. 
“Was anything withheld from the knowledge of Peter, who is called the rock on which the church should be built, who also obtained the keys of the kingdom of heaven, with the power of loosing and binding in heaven and on earth?” Tertullian, Prescription Against Heretics 22, 197-220 AD. 
“And that they [the Heretics] at first were believers in the doctrine of the Catholic Church, in the church of Rome under the episcopate of the blessed Eleutherus, until on account of their ever restless curiosity, with which they even infected the brethren, they were more than once expelled.” Tertullian, Prescription Against Heretics 30, 197-220 AD. 
“For this is the manner in which the apostolic churches transmit their registers: as the … church of Rome, which makes Clement to have been ordained [as a priest] in like manner by Peter.” Tertullian, Prescription Against Heretics 32, 197-220 AD. 
“Since, moreover, you are close upon Italy, you have Rome, from which there comes even into our own hands the very authority (of apostles themselves). How happy is its church, on which apostles poured forth all their doctrine along with their blood! Where Peter endures a passion like his Lord’s! Where Paul wins his crown in a death like John’s where the Apostle John was first plunged, unhurt, into boiling oil, and thence remitted to his island-exile!” Tertullian , Prescription Against Heretics 36, 197-220 AD. 
“Thus publicly announcing himself as the first among God’s chief enemies, he was led on to the slaughter of the apostles. It is, therefore, recorded that Paul was beheaded in Rome itself, and that Peter likewise was crucified under Nero. This account of Peter and Paul is substantiated by the fact that their names are preserved in the cemeteries of that place even to the present day. It is confirmed likewise by Caius, a member of the Church, who arose under Zephyrinus, bishop of Rome. He, in a published disputation with Proclus, the leader of the Phrygian heresy, speaks as follows concerning the places where the sacred corpses of the aforesaid apostles are laid: ‘But I can show the trophies of the apostles. For if you will go to the Vatican or to the Ostian way, you will find the trophies of those who laid the foundations of this church.’” Caius of Rome, Disputation with Proclus, 198 AD, quoted by Eusebius of Caesarea, Church History II:25:5-7, 340 AD. 
“Victor, who was the thirteenth bishop of Rome from Peter, but that from his successor,” Caius of Rome, The Little Labyrinth, 211 AD, quoted by Eusebius of Caesarea, Church History V:28:3, 340 AD. 
“Be it known to you, my lord [James, Bishop of Jerusalem], that Simon, who, for the sake of the true faith, and the most sure foundation of his doctrine, was set apart to be the foundation of the Church, and for this end was by Jesus Himself, with His truthful mouth, named Peter,” Pseudo-Clement, Letter of Clement to James 1, 221 AD. 
This letter is falsely attributed to St. Pope Clement, and we don’t know the true author. I have included it here, not because I believe that it is a legitimate Church Father, but because it portrays the beliefs of the Church at the time.
“[Simon Peter to Simon Magus] For in direct opposition to me, who am a firm rock, the foundation of the Church, you now stand.” Pseudo-Clement, Clementine Homilies XVII:19, 221 AD. 
“Look at [Peter], the great foundation of the Church, that most solid of rocks, upon whom Christ built the Church [Matt. 16:18]. And what does our Lord say to him? ‘Oh you of little faith,’ he says, ‘why do you doubt?’ [Matt. 14:31]” Origen, Homilies on Exodus V:4, 248 AD. 
“And, indeed, if we were to attend carefully to the evangelical writings, we would also find here, and in relation to those things which seem to be common to Peter and those who have thrice admonished the brethren, a great difference and a pre-eminence in the things said to Peter, compared with the second class. For it is no small difference that Peter received the keys not of one heaven but of more, and in order that whatsoever things he binds on the earth may be bound not in one heaven but in them all, as compared with the many who bind on earth and loose on earth, so that these things are bound and loosed not in the heavens, as in the case of Peter, but in one only; for they do not reach so high a stage, with power as Peter to bind and loose in all the heavens.” Origen, Commentary on Matthew XIII:31, 248 AD. 
“There is easy proof for faith in a short summary of the truth. The Lord speaks to Peter, saying, I say unto you, that you are Peter; and upon this rock I will build my Church, and the gates of hell shall not prevail against it. And I will give unto you the keys of the kingdom of heaven; and whatsoever you shall bind on earth shall be bound also in heaven, and whatsoever you shall loose on earth shall be loosed in heaven. And again to the same He says, after His resurrection, Feed my sheep. And although to all the apostles, after His resurrection, He gives an equal power, and says, As the Father has sent me, even so send I you: Receive the Holy Ghost: Whose soever sins you remit, they shall be remitted unto him; and whose soever sins you retain, they shall be retained (John 20:21) yet, that He might set forth unity, He arranged by His authority the origin of that unity, as beginning from one. Assuredly the rest of the apostles were also the same as was Peter, endowed with a like partnership both of honour and power; but the beginning proceeds from unity. Which one Church, also, the Holy Spirit in the Song of Songs designated in the person of our Lord, and says, My dove, my spotless one, is but one. She is the only one of her mother, elect of her that bare her (Song of Songs 6:9). Does he who does not hold this unity of the Church think that he holds the faith?” St. Cyprian of Carthage, Treatise I:4, 251 AD. 
This is a powerful quote. In summary, St. Cyprian of Carthage is saying that if anyone does not align themselves with the successor of St. Peter, then they can not be saved.
“There is one God, and Christ is one, and there is one Church, and one chair founded upon the rock by the word of the Lord. Another altar cannot be constituted nor a new priesthood be made, except the one altar and the one priesthood. Whosoever gathers elsewhere, scatters.” St. Cyprian of Carthage, Epistle XXXIX:5, 253 AD. 
“Cyprian to [Pope] Cornelius his brother, greeting… that letters should be sent you by all who were placed anywhere in the province; as in fact is done, that so the whole of our colleagues might decidedly approve of and maintain both you and your communion, that is as well to the unity of the Catholic Church as to its charity.” St. Cyprian of Carthage, Epistle XXXXIV:1, 3, 253 AD. 
“Cyprian to Antonianus his brother, greeting. I received your first letters, dearest brother, firmly maintaining the concord of the priestly college, and adhering to the Catholic Church, in which you intimated that you did not hold communion with Novatian, but followed my advice, and held one common agreement with [Pope] Cornelius our co-bishop. You wrote, moreover, for me to transmit a copy of those same letters to [Pope] Cornelius our colleague, so that he might lay aside all anxiety, and know at once that you held communion with him, that is, with the Catholic Church.” St. Cyprian of Carthage, Epistle LI:1, 253 AD. 
Communion with the Pope, says St. Cyprian of Carthage, is communion with the Catholic (read: Universal) Church which itself is a communion with Christ.
“Moreover, Cornelius was made bishop by the judgment of God and of His Christ, by the testimony of almost all the clergy, by the suffrage of the people who were then present, and by the assembly of ancient priests and good men, when no one had been made so before him, when the place of [Pope] Fabian, that is, when the place of Peter and the degree of the sacerdotal throne was vacant.” St. Cyprian of Carthage, Epistle LI:8, 253 AD. 
“After such things as these, moreover, they still dare— a false bishop having been appointed for them by, heretics— to set sail and to bear letters from schismatic and profane persons to the throne of Peter, and to the chief church whence priestly unity takes its source; and not to consider that these were the Romans whose faith was praised in the preaching of the apostle, to whom faithlessness could have no access.” St. Cyprian of Carthage, Epistle LIV:14, 253 AD. 
“Peter speaks there, on whom the Church was to be built, teaching and showing in the name of the Church, that although a rebellious and arrogant multitude of those who will not hear and obey may depart, yet the Church does not depart from Christ; and they are the Church who are a people united to the priest, and the flock which adheres to its pastor. Whence you ought to know that the bishop is in the Church, and the Church in the bishop; and if any one be not with the bishop, that he is not in the Church, and that those flatter themselves in vain who creep in, not having peace with God’s priests, and think that they communicate secretly with some; while the Church, which is Catholic and one, is not cut nor divided, but is indeed connected and bound together by the cement of priests who cohere with one another.” St. Cyprian of Carthage, Epistle LXVIII:8, 253 AD. 
“Thus Peter, the first of the apostles, having been often apprehended, and thrown into prison, and treated with igominy, was last of all crucified at Rome.” Peter of Alexandria, Canonical Epistles 9, 306 AD. 
I add quotes like this in to show St. Peter’s death in Rome, as there are many that deny that such a thing happened.
“And while Nero reigned, the Apostle Peter came to Rome, and, through the power of God committed unto him, wrought certain miracles, and, by turning many to the true religion, built up a faithful and steadfast temple unto the Lord. When Nero heard of those things, and observed that not only in Rome, but in every other place, a great multitude revolted daily from the worship of idols, and, condemning their old ways, went over to the new religion, he, an execrable and pernicious tyrant, sprung forward to raze the heavenly temple and destroy the true faith. He it was who first persecuted the servants of God; he crucified Peter, and slew Paul.” Lactiantius, Of the Manner in Which the Persecutors Died 2, 318 AD. 
So, what do all these quotes from the Ante-Nicean Church Fathers tell us about the papacy? They tell us that the Pope has ultimate teaching authority (Hermas, the Shepherd; St. Ignatius of Antioch, Epistle to the Romans; St. Justin Martyr, Dialogue of Justin with Trypho; Dionysius of Corinth, Letter to Pope Soter; St. Irenaeus of Lyons, Irenaeus Against Heresies; St. Clement of Alexandria, Fragments; Tertullian, Against Marcion; Tertullian, Prescription Against Heretics; St. Cyprian of Carthage, Treatise; St. Cyprian of Carthage, Epistles) as well as ultimate disciplinary authority (Hermas, the Shepherd; St. Ignatius of Antioch, Epistle to the Romans; Dionysius of Corinth, Letter to Pope Soter; St. Irenaeus of Lyons, Irenaeus Against Heresies; St. Irenaeus of Lyons, Fragments from the Lost Writings of Irenaeus; Tertullian, Prescription Against Heretics; St. Cyprian of Carthage, Treatise; St. Cyprian of Carthage, Epistles) and that his authority has primacy over the other bishops (St. Ignatius of Antioch, Epistle to the Romans; St. Irenaeus of Lyons, Irenaeus Against Heresies; St. Irenaeus of Lyons, Fragments from the Lost Writings of Irenaeus; Tertullian, Against Marcion; Tertullian, Prescription Against Heretics; Origen, Commentary on Matthew; St. Cyprian of Carthage, Treatise; St. Cyprian of Carthage, Epistles; Peter of Alexandria, Canonical Epistles). It also teaches us the historic reality that Christ established his Church on St. Peter (Tertullian, Against Marcion; Tertullian, Prescription Against Heretics; Pseudo-Clement, Letter of Clement to James; Pseudo-Clement, Clementine Homilies; Origen, Homilies on Exodus; St. Cyprian of Carthage, Treatise; St. Cyprian of Carthage, Epistles) and that he gave to St. Peter and his successors the keys to the kingdom (Tertullian, Prescription Against Heretics; Origen, Commentary on Matthew; St. Cyprian of Carthage, Treatise), and that St. Peter has successors (Hermas, the Shepherd; St. Clement of Rome, The First Epistle of Clement to the Corinthians; Dionysius of Corinth, Letter to Pope Soter; St. Irenaeus of Lyons, Irenaeus Against Heresies; Tertullian, Against Marcion; Tertullian, Prescription Against Heretics; Caius of Rome, Disputation with Proclus; Caius of Rome, The Little Labyrinth; St. Cyprian of Carthage, Epistles). It also teaches that salvation is impossible outside of communion with the Pope (St. Irenaeus of Lyons, Irenaeus Against Heresies; St. Irenaeus of Lyons, Fragments from the Lost Writings of Irenaeus; Tertullian, Against Marcion; Tertullian, Prescription Against Heretics; St. Cyprian of Carthage, Treatise; St. Cyprian of Carthage, Epistles). Also, papal infallibility (St. Justin Martyr, Dialogue of Justin with Trypho; Dionysius of Corinth, Letter to Pope Soter; St. Irenaeus of Lyons, Irenaeus Against Heresies; St. Clement of Alexandria, Fragments; Tertullian, Against Marcion; Tertullian, Prescription Against Heretics; St. Cyprian of Carthage, Treatise; St. Cyprian of Carthage, Epistles) and his association with Rome (St. Ignatius of Antioch, Epistle to the Romans; Dionysius of Corinth, Letter to Pope Soter; St. Irenaeus of Lyons, Irenaeus Against Heresies; St. Clement of Alexandria, Fragments; Tertullian, Against Marcion; Tertullian, An Answer to the Jews; Tertullian, Prescription Against Heretics; Caius of Rome, Disputation with Proclus; Caius of Rome, The Little Labyrinth; St. Cyprian of Carthage, Epistles; Peter of Alexandria, Canonical Epistles; Lactiantius, Of the Manner in Which the Persecutors Died) are also mentioned quite frequently. This is the summary of what the Ante-Nicean Church Fathers teach about one of the oldest doctrines of the Church, that of the Papacy.
A summary of the points:
The Sacred Scriptures, in union with the Sacred Tradition of the Fathers, possesses overwhelming testimony to the veracity of the claim of the Catholic Church, that she has continued to protect and defend the true faith of Christ. We see that the official Catholic teaching on the papacy, perfectly lines up with scripture and that which the Church Fathers wrote. Faced with such evidence, we must then turn to the only Church which has protected the true doctrines of Christianity, from the Church’s infancy, to the present day.
 Origen, Homilies on Genesis and Exodus, vol. 71 of The Fathers of the Church: A New Translation, trans. Ronald E. Heine. CUA Press, 2010.
Part I, where I go over the official Church teaching.
Part II, where I go over the Biblical evidence.
All scripture citations taken from the NRSVCE, the official liturgical scripture sanctioned by the Canadian Conference of Catholic Bishops (CCCB)
Addendum: In all things I submit to the authority of the Church if I have misrepresented any aspect of doctrine or history.