If their offspring were born in the United States, then they are Natural Born Citizens and eligible for the Presidency no matter how loathsome their fathers might have been.
Most importantly, however, they have to receive more votes than their opponents.
Not if their father (or mother) were a foreign national at the time of their birth. They would be considered citizens, but not NBC. The child would be born with foreign citizenship (allegiance)...in the case of being born to a British Subject. We know the framers wanted to prevent such foreign influence on the position of POTUS.