No. The law applies equally to everyone. Jefferson would have needed to have the child naturalized as an American citizen.
AmerAsian children are not even granted US citizenship automatically. Children born overseas to fathers serving their country in Vietnam or Korea have no rights to American citizenship or residency. As of 1987, now they are eligible for visa applications.
* Immigrant visas are issued to Amerasians under Public Law 100-202 (Act of 12/22/87), which provides for the admission of aliens born in Vietnam after January 1, 1962, and before January 1, 1976, if the alien was fathered by a U.S. citizen.
But an embassy is considered legally equivalent to American soil, no?
What if Jefferson’s wife were to have been an American citizen? Would it matter where their child was born?
What about a US army base?
What about military members in Germany with their American born spouses also in Germany who give birth to a child inside a US army hospital based in Germany?
By the way, several prominent Americans who have either been President or ran for President would not fit your view, why is that?
Here are a few;
President Chester Arthur had an Irish father who was not a US Citizen until his son was 14 years old.
Senator Barry Goldwater ran for President yet he was not born in a US State. He was born in a territory subject to US jurisdiction.
Senator and Governor Lowell P. Weicker ran for President in 1980 and was earlier considered a vice-presidential nominee in 1976. He was born in Paris, France, to parents who were U.S. citizens. His father was an American and his mother was born in India, the daughter of a British general.
John McCain was born in a territory subject to US jurisdiction.
There are others that appeared borderline eligible and who were supported by court rulings as eligible.
As for Ameriasian children, weren’t many of them born out of wedlock? So there was no clear record of their birth to members of the US military? I remember reading many American GI veterans in Vietnam were unaware they were fathers of children born to women they had relationships with.