According to Slavic gypsy tradition in the Balkans, one of the first things a vampire
would do after becoming embraced (that is, vampirized) was find and have sex with their new widow(er), sometimes even before the spouse was aware of their newly (un)dead state. When the vampire was female the union would be fruitless, but it was believed that male vampires were capable of impregnating living women. The resultant offspring were dhampir
s, children with half-vampire blood
This strange parentage conferred some interesting abilities (the ability to see often-invisible vampires) and disadvantages (er, bonelessness, a quality shared with all Eastern European vampires who are supposed to be quite spongy instead) on the children, who would often end up setting up shop as a kind of exorcist, using their unholy qualities to eradicate the ken of their blood-sucking parent through wrestling, sharpshooting and other, more esoteric rituals.
It was thought by some that dhampir blood was as persistant as vampire blood, and thus children (and grandchildren, etc.) of a dhampir would share its, er, ability to see vampires, bonelessness and proclivity towards going into the Ghostbusting business.
Variant names, depending on region and gender, for these adorable little softies included vampir for boys, vampuiera for girls, vampijerovic and lampijerovic.