Apostle John lived in Ephesus - what sources claim that? Which earliest sources does Christianity posses that claim that apostle John spent the last years of his life in Ephesus?
Revelation 1:9 explicitly states that John was on the island of Patmos when he wrote revelation:


  I, John, your brother and companion in the suffering and kingdom and patient endurance that are ours in Jesus, was on the island of Patmos because of the word of God and the testimony of Jesus.


That he would have been exiled there is common:


  "Early tradition says that John was banished to Patmos by the Roman authorities. This tradition is credible because banishment was a common punishment used during the Imperial period for a number of offenses. Among such offenses were the practices of magic and astrology. Prophecy was viewed by the Romans as belonging to the same category, whether Pagan, Jewish, or Christian. Prophecy with political implications, like that expressed by John in the book of Revelation, would have been perceived as a threat to Roman political power and order. Three of the islands in the Sporades were places where political offenders were banished." (Pliny Natural History 4.69-70; Tacitus Annals 4.30)[9]


Patmos is an island very close to the city of Ephesus, the major port city of the day.  Indeed, Revelation 2 - 3 is a series of letters to the 7 cities in Western Turkey, and Ephesus is by far the largest of them.  This is not surprising, since Rome pretty much cleared Jerusalem of Jews in 70AD (actually completely destroyed Jerusalem in 125AD!) thus resulting in a diaspora that moved many of the writers to Western Turkey and Galatia.  Indeed - every one of the Epistles written to a city or region in Turkey or Greece.

Were we to receive word that a certain person was familiar with the Bronx, Manhattan, Newark, Hoboken, and we have written correspondance to them where he claims to be at Hsing Hsing prison - especially absent any transportation - it would not at all be unreasonable to assume he is from New York.

When tradition thus states that John was living in the biggest city of the area, and we have written correspndance that shows how close he was, it's a really safe bet.