These are the three that immediately come to mind:
In I Hunt Killers, Jazz Dent is the son of Billy Dent, one of the most notorious killers of the century. Jazz is worried that he'll follow in his father's footsteps, desperate to prove that he won't... but is very aware of the fact that he has, well, urges. Loved it SO MUCH.
In Ripper, 14-year-old orphan Carver Young learns that his father might A) be alive and well, B) Jack the Ripper, and C) killing again.
In Slice of Cherry, Kit and Fancy Cordelle are the daughters of the Bonesaw Killer. And they take after him, big time.