In his book History and Christianity: A Vigorous, Convincing Presentation of the Evidence for a Historical Jesus (1965, IVP Press), John Warwick Montgomery says on page 34:
Irenaeus had often heard from Polycarp the eyewitness accounts of Jesus received from John and others who had been personally acquainted with Jesus.13
13See Eusebius, H.E., V. 20.
At face value, I found this, combined with Irenaeus' reference to the Gospels, to be the most powerful point in Montgomery's book. However, Polycarp himself does not claim to have known John or others who new Jesus, and his biographer does not mention this either. So we could say that Irenaeus claims a connection to Jesus, but Polycarp does not.
Unfortunately, the only other example Montgomery provides is Paul. Are there others who claim a connection to Jesus? (Such as Irenaeus, who studied under Polycarp, who met John, who was a disciple of Jesus)