Is Hellboy the son of the Devil?

No. In the original lore, Hellboy is the son of a demon called Azzael and a 16th century witch named Sarah Hughes. In the lore, Azzael is the duke of Hell who influences a witch resulting in the birth of Hellboy. Unlike Hellboy, Azzael is clearly malevolent and kidnaps Sarah when she tries to repent of witch craft and drags her to Hell.

After he burns her to death, he takes their child, Hellboy, cuts off his hand and replaces it with the legendary hand of doom. After doing this Azzael is stripped of his power and imprisoned in ice. Azzael’s name is probably based on the Hebrew name Azazel, a mysterious demonic entity mentioned in the Hebrew Torah in Leviticus 16. It may have been a literal demon, or a rugged mountain cliff that the goat designated as the scapegoat by the Jewish priest was sent to be released into the wilderness. Either way, it makes a good name for a demon.