That is incorrect. Barron Trump was born on March 20, 2006. Melania Trump became a U.S. citizen on July 28, 2006. So, Tiffany Trump is his only child born to a U.S. citizen mother.
American women couldn't even pass on citizenship until the Cable act of 1922.
Citizenship in America has always revolved around the father, and the mother didn't matter at all. If she married an American, she was automatically a citizen, and one that couldn't vote for most of our existence.