The authoritative and unbroken transmission of the mission and powers conferred by Jesus Christ on St. Peter and the Apostles from them to the present pope and hierarchy.
2 Chr. 19:11 – And behold, Amariah the chief priest is over you in all matters of the LORD; and Zebadiah the son of Ishmael, the governor of the house of Judah, in all the king’s matters; and the Levites will serve you as officers. Deal courageously, and may the LORD be with the upright!”
Mal. 2:7 – For the lips of a priest should guard knowledge, and men should seek instruction from his mouth, for he is the messenger of the LORD of hosts.
Eph. 2:19-20 – So then you are no longer strangers and sojourners, but you are fellow citizens with the saints and members of the household of God, 20 built upon the foundation of the apostles and prophets, Christ Jesus himself being the cornerstone.
Eph. 4:11 – And his gifts were that some should be apostles, some prophets, some evangelists, some pastors and teachers…
1 Cor. 12:28-29 – And God has appointed in the church first apostles, second prophets, third teachers, then workers of miracles, then healers, helpers, administrators, speakers in various kinds of tongues. 29 Are all apostles? Are all prophets? Are all teachers? Do all work miracles?
Acts 1:20 – For it is written in the book of Psalms, ‘Let his habitation become desolate, and let there be no one to live in it’; and ‘His office let another take.’
1 Tim. 3:1; 5:17 – Paul, an apostle of Christ Jesus by command of God our Savior and of Christ Jesus our hope… Let the elders who rule well be considered worthy of double honor, especially those who labor in preaching and teaching.
1 Tim. 5:22 – Do not be hasty in the laying on of hands, nor participate in another man’s sins; keep yourself pure.
Acts 14:23 – And when they had appointed elders for them in every church, with prayer and fasting they committed them to the Lord in whom they believed.
2 Tim 2:2 – and what you have heard from me before many witnesses entrust to faithful men who will be able to teach others also.
Tit. 1:5 – This is why I left you in Crete, that you might amend what was defective, and appoint elders in every town as I directed you,…
Patristic testimony is not unanimous about the order of succession to St. Peter as Bishop of Rome. The old list of the popes, hitherto based on the Liber Pontificalis, gave the papal succession as: Linus, Cletus, Clement, Anacletus (Loomis, Book of Popes). Tertullian implied that Clement was the second pope (Prescriptions, 32); and St. Optatus listed: Linus, Cletus, Anacletus, Clement, while the Poem Against Marcion gave: Linus, Cletus, Anacletus, Clement. But in 1947 the quasi-official list of the Annuario Pontificio was changed in accord with the testimony of St. Irenæus of Lyons: “The blessed apostles founded and reared this church and afterwards committed unto Linus the office of the episcopate. This same Linus is mentioned by Paul in his Epistles to Timothy (2 Tim. 4:21). His successor was Anacletus, after whom, in the third place from the apostles, Clement was elected to the bishopric” (Against Heresies, III, 3). This is both the earliest and most reliable evidence. Modern historians now practically agree that Cletus and Anacletus were two names of the same man-like Saul and Paul -and that earlier annalists made two popes out of one. Eusebius, after weighing the early evidence, accepted St. Irenæus’s list, to which he supplied dates. Eusebius’s chronology, which can be only approximately accurate, would give: St. Linus (67-79), St. Anacletus (79-91), St. Clement (91-100), and St. Evaristus (100-108).[1]
St. Cyprian of Carthage [AD 251/156] “Our Lord, whose commands we ought to fear and observe, says in the Gospel, by way of assigning the episcopal dignity and settling the plan of his Church: ‘I say to you, that you are Peter, and on this rock will I build my Church, and the gates of hell will not overcome it. And to you I will give the keys of the kingdom of heaven: and whatever you bind on earth will be bound also in heaven, and whatever you loose on earth they will be loosed in heaven.’ From that time the ordination of bishops and the plan of the Church flows on through the changes of times and successions; for the Church is founded upon the bishops, and every act of the Church in controlled by these same rulers” (Cyprian to the lapsed – Epistle 25, 1).
St. Clement of Rome [AD 80] “Through countryside and city [the apostles] preached; and they appointed their earliest converts, testing them by the Spirit, to be the bishops and deacons of future believers. Nor was this a novelty, for bishops and deacons had been written about a long time earlier” (Epistle to the Corinthians 42:4-5).
St. Ignatius of Antioch [AD 107] “Take care to do all things in harmony with God, with the bishop presiding in the place of God and with the presbyters in the place of the council of the apostles, and with the deacons, who are most dear to me” (Letter to the Magnesians 6:1).
[1] Eberhardt, Catholic Church History.