In his Church History , Eusebius makes it clear that he believes that John was exiled to Patmos during the reign of Domitian.

In the Demonstration of the Gospel (3.5), he perhaps implies something else. He summarizes the persecutions of Christians that began with Stephen in this way: “Herod again later on, the King of the Jews, killed James the brother of John with the sword, and cast Peter into prison, as is written in the Acts of the Apostles. And yet, though they had suffered thus, the rest of the disciples held tenaciously to Jesus, and were still more diligent in preaching to all of Him and His miracles. Afterwards James, the Lord’s brother, whom of old the people of Jerusalem called ‘the Just’ for his extraordinary virtue, being asked by the chief priests, and teachers of the Jews what he thought about Christ, and answering that He was the Son of God, was also stoned by them. Peter was crucified head downwards at Rome, Paul beheaded, and John exiled to an island. Yet though they suffered thus, not one of the others gave up his intention, but they made their prayer to God that they themselves might suffer a like fate for their religion, and continued to bear witness to Jesus and His marvellous works with yet more boldness.”

Here he puts John’s exile in a line with Peter’s crucifixion and Paul’s beheading. He doesn’t indicate explicitly either the time or the place, but he leaves the impression that John’s exile followed close on the heels of the deaths of the other apostles.