Here’s some other great stuff from around 96 AD.
This letter from Clement to the Corinthians supports the Catholic Church’s position in several ways, but the two primary points in my opinion are that it is clear that the Corinthians sought Clement’s intervention and he in turn described apostolic succession just as it is understood today by the Catholic Church.
Clement is believed to be the fourth pope(it is possible he was the third). He was writing to the Corinthians regarding some Bishops who had been removed from authority without proper procedures. He instructed the Corinthians to leave them in power and we know from later writings that they complied and were pleased to receive his letter.
Chapter 42. The Order of Ministers in the Church.
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.
Chapter 44. The Ordinances of the Apostles, that There Might Be No Contention Respecting the Priestly Office.
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. We are of opinion, therefore, that those appointed by them, or afterwards by other eminent men, with the consent of the whole church, and who have blamelessly served the flock of Christ, in a humble, peaceable, and disinterested spirit, and have for a long time possessed the good opinion of all, cannot be justly dismissed from the ministry. For our sin will not be small, if we eject from the episcopate those who have blamelessly and holily fulfilled its duties. Blessed are those presbyters who, having finished their course before now, have obtained a fruitful and perfect departure [from this world]; for they have no fear lest any one deprive them of the place now appointed them. But we see that you have removed some men of excellent behaviour from the ministry, which they fulfilled blamelessly and with honour.
More here:
newadvent.org/fathers/1010.htm