Is a father considered an infidel for denying the existence of jinn, and if so, is his son considered illegitimate due to the invalidity of his parents' marriage?

Denying the existence of jinn is outright disbelief (kufr sareeh), because it entails rejecting the Qur’an and the verses mentioned therein that speak of jinn, and an entire surah is even named after them. As for someone who affirms the word "jinn" in the Qur’an but interprets it to mean something other than its true reality, their misconception is first addressed, and the proof is established against them. As for the matter of lineage, there is no problem with it. A son is not described as a child of fornication even if his father apostatizes, and his lineage remains established. If a Muslim woman conceives a child with an apostate, the child is Muslim, following the religion of his mother.