Did Antony and Cleopatra Live in Ephesus?

No, but they may have first met each other there when she accompanied her father, Ptolemy XII Auletes, to join forces with Gabinus, a subordinate of Julius Caesar. They never lived there, but Cleopatra's treacherous sister Arsinoe was in exile on Ephesus, and created a lot of trouble in spreading rumours that Mark Antony was a traitor to Cleopatra during her backing of him and Octavian during the brief insurrection by Cassius and Brutus following the assassination of Julius Caesar. Arsinoe was herself killed on the steps of the Temple of Artemis in approx. 40 BC, but Antony and Cleopatra never lived there.