"I mean - father-son issues, I have them. But, on the whole, I'd rather be a Malfoy than, you know, the son of the Dark Lord."
--Scorpius Malfoy (CC1.3)
The Rumor of Voldemort’s Heir suggests that Voldemort fathered a child before he died.
There have been numerous versions of this narrative (CC1.4, CC1.12), but one common version concerned the Malfoy family. The rumor was that Draco and Astoria Malfoy were unable to have children to carry on the Malfoy bloodline and that Astoria travelled back in time to conceive a child with Voldemort. The rumor that Voldemort was his father made things difficult for Scorpius Malfoy at Hogwarts (CC1.3) His father, Draco, was also bothered by the rumor, and tried to get the Ministry to help him quash it (CC1.4, CC1.12).
After being told by Rodolphus Lestrange that she was the daughter of Voldemort and Bellatrix, Delphi embraced that identity (CC4.11).