>>15358181U.S. Supreme Court specifically addressed this in United States v. Bhagat Singh Thind (1923) wherein SCOTUS unanimously ruled that pajeets cannot be citizens of the United States, retroactively invalidating citizenship of any dot indians.
British-born Justice George Sutherland wrote for unanimous Court that "Aryan theory" has no credibility, and being "Aryan" or "Caucasian" does not mean White (i.e. eligible to be an American).