Between A.D. 95 and about 165, a number of works were written by men who had known the apostles and the apostolic doctrine; they are known as the Apostolic Fathers.
Ignatius of Antioch [c.35-50 – c. 98-117 AD] also known as Ignatius Theophorus was an early Christian writer and bishop of Antioch. While en route to Rome, where he met his martyrdom, Ignatius wrote a series of letters.
Papias was a Greek Apostolic Father, Bishop of Hierapolis, and author who lived c. 60 – c. 135 AD. He wrote the Exposition of the Sayings of the Lord in five books.
Clement of Rome belongs to a group of early church leaders that have been known since the seventeenth century as the “Apostolic Fathers.”
The epistle was written in the name of the Roman Church to the Christian brotherhood at Corinth. The author was Clement, the Bishop of the Roman Christians, but he does not write in his own name.
There is much in-depth information in this article: The Synoptic Gospels in the Ancient Church: The Testimony to the Priority of the Gospel of Matthew. We have a brief introduction to papyrus from Tyndale Bible Dictionary. We have a lengthy apologetic article on Papias and the arguments from higher critics by F. David Farnell. This is followed by Papias' writings from two leading scholars on the Apostolic Fathers, Michael W. Holmes, and J. B. Lightfoot.