Only naturalized citizenship. It's in the Constitution, you've heard of that I'm sure. Specifically Article I, Section 8 which reads in part;
The Congress shall have Power
To establish an uniform Rule of Naturalization
Nothing in section 8 or anywhere else about Congress setting standards for citizenship. The 14th amendment to the constitution does say that
Section. 1. All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside.
While Article II section 1 says in part
No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President;
You may assume that "citizen at birth" is the same as "natural born citizen", but no Court has ruled on that subject, with regards to 14th amendment citizens at birth. Nor on exactly what "natural born citizen" might mean, well except for one case where a baby born in the US of Naturalized parents from Sweden, was declared a natural born citizen, even though when she was about 4 her mother took her to Sweden, joined later by her father, and they never returned to the US, although she did. However it was really only her citizenship was in question in the case. It was the DC Circuit that declared her natural born, while the Supreme Court upheld her citizenship, directing the Secretary of State to admit her and issue her a US Passport. Elg was her last name.