Being apostolic would mean that they retained the teachings of the apostle. Even Today, with all of the manuscripts and historical evidence, it is still difficult to determine just how closely the teachings of the Apostolic Fathers resembled to or agreed with Jesus’ teachings. The objective of these men was undoubtedly altruistic (noble), seeking to protect or support (make known) a certain orthodox Christianity. They denounced idolatry and loose morals. They believed that Jesus is the divine Son of God and that he was resurrected. However, they were not able to hold back the growing wave of apostasy. Sadly, being honest, some of them contributed to it.
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.
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.