St. Clement I on Apostolic Succession

The apostles have preached the Gospel to us from the Lord Jesus Christ; Jesus Christ has done so from God. Christ therefore was sent forth by God, and the apostles by Christ. Both these appointments, then, were made in an orderly way, according to the will of God. Having therefore received their orders, and being fully assured by the resurrection of our Lord Jesus Christ, and established in the word of God, with full assurance of the Holy Ghost, they went forth proclaiming that the kingdom of God was at hand. And thus preaching through countries and cities, they appointed the first-fruits of their labours, having first proved them by the Spirit, to be bishops and deacons of those who should afterwards believe…Our apostles also knew, through our Lord Jesus Christ, and 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 presbyters already mentioned, and afterwards gave instructions, that when these should fall asleep, other approved men should succeed them in their ministry.

St. Clement I – First Epistle to the Church at Corinth, Ch 42 & 44, A.D. 96

St. Isidore on Apostolic Authority

We, as Catholics are not permitted to believe anything of our own will, nor to choose what someone has believed of his. We have God’s apostles as authorities, who did not themselves of their own wills choose anything of what they wanted to believe, but faithfully transmitted to the nations, the teachings of Christ.

St. Isidore of Seville – 560 to 636 A.D.

St. Augustine on the Papacy and Apostolic Succession

In the Catholic Church, there are many other things which most justly keep me in her bosom. The consent of peoples and nations keeps me in the Church; so does her authority, inaugurated by miracles, nourished by hope, enlarged by love, established by age. The succession of priests keeps me, beginning from the very seat of the Apostle Peter, to whom the Lord, after His resurrection, gave it in charge to feed His sheep (Jn 21:15-19), down to the present episcopate.

St. Augustine (354–430): Against the Epistle of Manichaeus called Fundamental, chapter 4: Proofs of the Catholic Faith

St. Irenaeus on the successors to Peter preserving the one true faith

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, exhorting them to peace, renewing their faith, and declaring the tradition which it had lately received from the apostles, proclaiming the one God, omnipotent, the Maker of heaven and earth, the Creator of man, who brought on the deluge, and called Abraham, who led the people from the land of Egypt, spoke with Moses, set forth the law, sent the prophets, and who has prepared fire for the devil and his angels. From this document, whosoever chooses to do so, may learn that He, the Father of our Lord Jesus Christ, was preached by the Churches, and may also understand the tradition of the Church, since this Epistle is of older date than these men who are now propagating falsehood, and who conjure into existence another god beyond the Creator and the Maker of all existing things. 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.

Against Heresies III.3.3 by St. Irenaeus