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.
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.
Clement of Rome belongs to a group of early church leaders that have been known since the seventeenth century as the “Apostolic Fathers.”
When the disciples realized that they had seen the risen Christ for the last time and that it had now become their duty to spread His message, they gathered themselves together and restored the number of "witnesses" to the appointed Twelve. Immediately afterward the outpouring of the Holy Spirit gave them the signal to begin work.