In 2373, when Bashir time traveled to 2268 and visited the USS Enterprise, he encountered one of the ship's crewmembers, named Lieutenant Watley. After having learned of Watley's name, he began to suspect that he was experiencing a predestination paradox. He recalled that nobody had ever met his great-grandfather, and suggested to Miles O'Brien that he was destined to fall in love with Lt. Watley and become his own ancestor.
Bashir was rebuffed by O'Brien, who felt that he was simply attempting to justify his attraction to her. Bashir's suspicions turned out to be unfounded, however, in that his failure to pursue a relationship with Watley resulted in no alterations to the timeline. (DS9: "Trials and Tribble-ations")