The most cited passage employed as evidence that the early Christians placed John’s exile and apocalyptic vision (of Revelation) late in the first century, late in Domitian’s reign, is found in Irenaeus:
Had there been any need for his name to be openly announced at the present time, it would have been stated by the one who saw the actual revelation. For it was seen not a long time back, but almost in my own lifetime, at the end of Domitian’s reign.Against Heresies, 5.30.3
This is the standard translation (concerning the question of whether the subject was John instead (“he was seen”), see here).
Sometimes on websites it is claimed that when Irenaeus spoke of Domitian, he was actually referring to Nero, so that Irenaeus claimed that the apocalyptic vision was seen late in Nero’s reign.
The argument is that the “Domitianou” in “Domitian’s reign” is adjectival because it lacks an article, and that it therefore refers to Domitius, which was one of the birth names of Nero (Nero’s birth name was Lucius Domitius Ahenobarbus).
This argument was first propounded by the German scholar Guericke in 1843, but it has not found any support in subsequent scholarship.
This argument seems to have been taken up by Robert Young (who was self-taught) in 1865; Young’s argument was subsequently quoted by Foy E. Wallace (a preacher in the “Church of Christ,” who did not have any formal academic training) in his commentary on Revelation (1966), and it is via Wallace’s commentary that Young’s quotation has become more widely known.
It was written in Patmos about A. D. 68, whither John had been banished by Domitius Nero, as stated in the title of the Syriac version of the book; and with this concurs the express statement of Irenaeus in A. D. 175, who says it happened in the reign of Domitianou–i.e., Domitius (Nero). Sulpicius, Orosius, etc., stupidly mistaking Domitianou for Domitianikos, supposed Irenaeus to refer to Domitian, A. D. 95, and most succeeding writers have fallen into the same blunder. The internal testimony is wholly in favor of the earlier date.Robert Young, Concise Commentary on the Holy Bible, 179.*
Concerning Guericke’s proposal, Farrar wrote back in 1888:
Guericke proposes to take “Dometianou” as an adjective, and to render the clause “near the close of the Domitian rule,” i.e., the rule of Domitius Nero”. But the absence of the article on which he relies gives no support to his view, and no scholar will accept this hypothesis, though he may admit the possibility of some confusion between the names Domitius and Domitian.F. W. Farrar, The Early Days of Christianity (New York: Funk & Wagnalls, 1888), 407
The theory that Irenaeus was using an adjectival form of Domitius seems to have not even received a mention in scholarly works written in the past century.
The theory is also disproved by Josephus, who has similar wording in a passage that indisputably refers to Domitian:
In both cases, the genitive of the name Domitian is without the article, yet we can see from Josephus that this does not render the name adjectival.
 Heinrich Ernst Ferdinand Guericke, Historisch-kritische Einleitung in das Neue Testament (Leipzig, 1843), 285 n. 4.