The testimony of early Christian writers is almost unanimous that the book of Revelation was written during the reign of Domitian. For example:
Irenaeus (c. A.D. 130 - c. 202), who had met Polycarp who had personally known John, wrote that "the apocalyptic vision . . . was seen no very long time since, but almost in our day, towards the end of Domitian's reign" (Against Heresies, Book V, Chapter 30, number 3; Ante-Nicene Fathers, vol. 1, pp. 559, 560).
Victorinus (died c. A.D. 303) wrote, "When John said these things he was in the island of Patmos, condemned to the labor of the mines by Caesar Domitian" (Commentary on the Apocalypse, on Rev. 10:11; Ante-Nicene Fathers, vol. 7, p. 353).
Eusebius (died c. A.D. 340) wrote, "But after Domitian had reigned fifteen years, and Nerva had succeeded to the empire, the Roman Senate, according to the writers that record the history of those days, voted that Domitian's honors should be canceled, and that those who had been unjustly banished should return to their homes and have their property restored to them. It was at this time that the apostle John returned from his banishment in the island and took up his abode at Ephesus, according to an ancient Christian tradition" (Ecclesiastical History, Book 3, Chapter 20).
The opinion that John's exile took place during the reign of Nero (A.D. 54-68) or Vespasian (A.D. 69-79) is held by those who wish to identify Nero as the beast of Revelation 13 and 17. But that interpretation, lacking objective evidence, has been rejected by most scholars.