St. Jerome: If, however, Jovinianus should obstinately contend that John was not a virgin, (whereas we have maintained that his virginity was the cause of the special love our Lord bore to him), let him explain, if he was not a virgin, why it was that he was loved more than the other Apostles. But you say, Matthew 16:18 the Church was founded upon Peter: although elsewhere the same is attributed to all the Apostles, and they all receive the keys of the kingdom of heaven, and the strength of the Church depends upon them all alike, yet one among the twelve is chosen so that when a head has been appointed, there may be no occasion for schism.- Against Jovianus, Book I: 26.
“Just as he himself gave the light to the apostles, so that the light of the world would be addressed, and the rest [of the apostles’] names are chosen by the Lord: and thus to Simon, who believed in Christ the Rock, the name of Peter is imparted. But following the metaphor of the rock, rightly it is said to him: “I will build my Church upon you.”- Commentarioum In Evangelium Matthaei Ad Eusebium Libri Quatuor,Patrologia Latina 26: 0117C – 0117D.
St. Hilary of Poitiers: A belief that the Son of God is Son in name only and not in nature, is not the faith of the Gospels and of the Apostles. If this be a mere title, to which adoption is His only claim; if He be not the Son in virtue of having proceeded forth from God, whence, I ask, was it that the blessed Simon Bar-Jona confessed to Him, You are the Christ, the Son of the living God Matthew 16:16 ? Because He shared with all mankind the power of being born as one of the sons of God through the sacrament of regeneration? If Christ be the Son of God only in this titular way, what was the revelation made to Peter, not by flesh and blood, but by the Father in heaven? What praise could he deserve for making a declaration which was universally applicable? What credit was due to Him for stating a fact of general knowledge? If He be Son by adoption, wherein lay the blessedness of Peter’s confession, which offered a tribute to the Son to which, in that case, He had no more title than any member of the company of saints? The Apostle’s faith penetrates into a region closed to human reasoning. He had, no doubt, often heard, He that receives you receives Me, and He that receives Me receives Him that sent Me. Matthew 10:40 Hence he knew well that Christ had been sent; he had heard Him, Whom he knew to have been sent, making the declaration, All things are delivered unto Me of the Father, and no one knows the Son but the Father, neither knows any one the Father save the Son. What then is this truth, which the Father now reveals to Peter, which receives the praise of a blessed confession? It cannot have been that the names of ‘Father’ and ‘Son’ were novel to him; he had heard them often. Yet he speaks words which the tongue of man had never framed before:— You are the Christ, the Son of the living God. For though Christ, while dwelling in the body, had avowed Himself to be the Son of God, yet now for the first time the Apostle’s faith had recognised in Him the presence of the Divine nature. Peter is praised not merely for his tribute of adoration, but for his recognition of the mysterious truth; for confessing not Christ only, but Christ the Son of God. It would clearly have sufficed for a payment of reverence, had he said, You are the Christ, and nothing more. But it would have been a hollow confession, had Peter only hailed Him as Christ, without confessing Him the Son of God. And so his words You are declare that what is asserted of Him is strictly and exactly true to His nature. Next, the Father’s utterance, This is My Son, had revealed to Peter that he must confess You are the Son of God, for in the words This is, God the Revealer points Him out, and the response, You are, is the believer’s welcome to the truth. And this is the rock of confession whereon the Church is built. But the perceptive faculties of flesh and blood cannot attain to the recognition and confession of this truth. It is a mystery, Divinely revealed, that Christ must be not only named, but believed, the Son of God. Was it only the Divine name; was it not rather the Divine nature that was revealed to Peter? If it were the name, he had heard it often from the Lord, proclaiming Himself the Son of God. What honour, then, did he deserve for announcing the name? No; it was not the name; it was the nature, for the name had been repeatedly proclaimed.
This faith it is which is the foundation of the Church; through this faith the gates of hell cannot prevail against her. This is the faith which has the keys of the kingdom of heaven. Whatsoever this faith shall have loosed or bound on earth shall be loosed or bound in heaven. This faith is the Father’s gift by revelation. – On the Trinity, Book VI: 36
Had ye seen, O holy and blessed men (the apostles), who for the reward of your faith have received the keys of the kingdom of heaven and power to bind and to loose in heaven and earth, works so great, so truly Divine, wrought by our Lord Jesus Christ, the Son of God; and do ye yet profess that it was not until He had first told you that He had gone forth from God that you attained the knowledge of the truth? – On the Trinity 6.33
St. Cyprian: Our Lord, whose precepts and admonitions we ought to observe, describing the honour of a bishop and the order of His Church, speaks in the Gospel, and says to Peter: “I say unto thee, That thou art Peter, and upon this rock will I build my Church … Thence, through the changes of times and successions, the ordering of bishops and the plan of the Church flow onwards; so that the Church is founded upon the bishops, and every act of the Church is controlled by these same rulers. Since this, then, is founded on the divine law, I marvel that some, with daring temerity, have chosen to write to me as if they wrote in the name of the Church; when the Church is established in the bishop and the clergy, and all who stand fast in the faith… And this unity we ought firmly to hold and assert, especially those of us that are bishops who preside in the Church, that we may also prove the episcopate itself to be one and undivided … The episcopate is one, each part of which is held by each one for the whole…” Epistle XXVI, 258 A.D.
St. Augustine quoting Cyprian: “For neither did Peter, whom the Lord chose first, and on whom He built His Church, when Paul afterwards disputed with him about circumcision, claim or assume anything insolently and arrogantly to himself, so as to say that he held the primacy, and should rather be obeyed of those who were late and newly come.”
Here is a passage in which Cyprian records what we also learn in holy Scripture, that the Apostle Peter, in whom the primacy of the apostles shines with such exceeding grace, was corrected by the later Apostle Paul, when he adopted a custom in the matter of circumcision at variance with the demands of truth. If it was therefore possible for Peter in some point to walk not uprightly according to the truth of the gospel … For who can be ignorant that the primacy of his apostleship is to be preferred to any episcopate whatever? But, granting the difference in the dignity of their sees, yet they have the same glory in their martyrdom … Wherefore, if Peter, on doing this, is corrected by his later colleague Paul, and is yet preserved by the bond of peace and unity till he is promoted to martyrdom, how much more readily and constantly should we prefer, either to the authority of a single bishop, or to the Council of a single province, the rule that has been established by the statutes of the universal Church?” ~ On Baptism Against the Donatists
St. John Chrysostom: But since I have mentioned Peter, I have perceived a fifth crown woven from him, and this is that this man succeeded to the office after him. For just as any one taking a great stone from a foundation hastens by all means to introduce an equivalent to it, lest he should shake the whole building, and make it more unsound, so, accordingly, when Peter was about to depart from here, the grace of the Spirit introduced another teacher equivalent to Peter, so that the building already completed should not be made more unsound by the insignificance of the successor.” – Homilies on St. Ignatius, Chapter 4
Council of Constantinople: The bishops are not to go beyond their dioceses to churches lying outside of their bounds, nor bring confusion on the churches; but let the Bishop of Alexandria, according to the canons, alone administer the affairs of Egypt; and let the bishops of the East manage the East alone, the privileges of the Church in Antioch, which are mentioned in the canons of Nicea, being preserved; and let the bishops of the Asian Diocese administer the Asian affairs only; and the Pontic bishops only Pontic matters; and the Thracian bishops only Thracian affairs.” – Philip Schaff: NPNF2-14. The Seven Ecumenical Councils – Christian Classics Ethereal Library.
The Council of Nicea: Let the ancient customs in Egypt, Libya and Pentapolis prevail, that the Bishop of Alexandria have jurisdiction in all these, since the like is customary for the Bishop of Rome also. Likewise in Antioch and the other provinces, let the Churches retain their privileges. And this is to be universally understood, that if any one be made bishop without the consent of the Metropolitan, the great Synod has declared that such a man ought not to be a bishop. If, however, two or three bishops shall from natural love of contradiction, oppose the common suffrage of the rest, it being reasonable and in accordance with the ecclesiastical law, then let the choice of the majority prevail. – 325 A.D., Canon 6.
St. Gregory of Narek: “For verily, as Peter’s open profession of faith in the Trinity earned for him the blessed name, Rock, so in expectation of your clemency, do I, a sinner condemned, await exoneration, O deliverer of captives.” – (Speaking with God from the Depths of the Heart: Prayer 13, B).