STATUS: Technically False
It is often rumored that Kieron Dwyer is the son of John Byrne. They are not blood relatives, but Byrne DID marry Dwyer's mother, photographer Andrea Braun, in 1980, when Dwyer was 13 (Byrne and Braun have since divorced).
As Dwyer retells it (in this Jon Ellis interview), "I was just getting into Byrne's art when my Mom met him at a convention in Chicago. She had brought me down there to check it out (my first convention!), and the rest, as they say, is history."
Dwyer elaborated on the relationship, and whatever help Byrne gave him in his entry into the comic business, in this interview with Michael Thomas: