Is that part of the constitution?
Nope.
It was written about 1760. Widely known amongst the founders, and relied on by numerous Supreme Court cases. (including The Venus, US 12 253 and another decision I have found which came out of Pennsylvania about 1788).
So take it for what it’s worth. According to Vattel, in dubious cases like this one, the child is the son of the father, and follows his fathers rights and duties.