“Paternal counts for nothing, unless you’ve got a lab far beyond the ken of the 18th century!”
Natural born citizenship in Western cultures have always required a citizen father within the jurisdiction of the sovereign for status as a natural born citizen since the days of the Roman Republic and the Greek city states. Descent of citizenship was rare, but it did exist for subjects of the Roman sovereignty. Acquisition of citizenship by descent from a citizen mother has never existed in English, British, or U.S. jurisdictions except by naturalization, and in the United States this naturalization has only been available since the 1934 change in the naturalization law.
That was long before Watson and Crick discovered DNA in 1953 (with insufficiently acknowledged help from XX Rosalind Franklin (died at 37 from ovarian cancer)).
Facts trump law, although you may need an election or two to force it (XXs outnumber XYs).