Supreme Court cases that cite natural born Citizen as one born on U.S. soil to citizen parents:
The Venus, 12 U.S. 8 Cranch 253 253 (1814)
Vattel, who, though not very full to this point, is more explicit and more satisfactory on it than any other whose work has fallen into my hands, says: The citizens are the members of the civil society; bound to this society by certain duties, and subject to its authority, they equally participate in its advantages. The natives or indigenes are those born in the country of parents who are citizens. Society not being able to subsist and to perpetuate itself but by the children of the citizens, those children naturally follow the condition of their fathers, and succeed to all their rights.
Shanks v. Dupont, 28 U.S. 3 Pet. 242 242 (1830)
Ann Scott was born in South Carolina before the American revolution, and her father adhered to the American cause and remained and was at his death a citizen of South Carolina. There is no dispute that his daughter Ann, at the time of the Revolution and afterwards, remained in South Carolina until December, 1782. Whether she was of age during this time does not appear. If she was, then her birth and residence might be deemed to constitute her by election a citizen of South Carolina. If she was not of age, then she might well be deemed under the circumstances of this case to hold the citizenship of her father, for children born in a country, continuing while under age in the family of the father, partake of his national character as a citizen of that country. Her citizenship, then, being prima facie established, and indeed this is admitted in the pleadings, has it ever been lost, or was it lost before the death of her father, so that the estate in question was, upon the descent cast, incapable of vesting in her? Upon the facts stated, it appears to us that it was not lost and that she was capable of taking it at the time of the descent cast.
Dred Scott v. Sandford, 60 U.S. 393 (1857)
The citizens are the members of the civil society; bound to this society by certain duties, and subject to its authority, they equally participate in its advantages. The natives, or natural-born citizens, are those born in the country, of parents who are citizens. As society cannot perpetuate itself otherwise than by the children of the citizens, those children naturally follow the condition of their parents, and succeed to all their rights.' Again: 'I say, to be of the country, it is necessary to be born of a person who is a citizen; for if he be born there of a foreigner, it will be only the place of his birth, and not his country. . . .
Minor v. Happersett , 88 U.S. 162 (1875)
The Constitution does not in words say who shall be natural-born citizens. Resort must be had elsewhere to ascertain that. At common law, with the nomenclature of which the framers of the Constitution were familiar, it was never doubted that all children born in a country of parents who were its citizens became themselves, upon their birth, citizens also. These were natives or natural-born citizens, as distinguished from aliens or foreigners. Some authorities go further and include as citizens children born within the jurisdiction without reference to the citizenship of their parents. As to this class there have been doubts, but never as to the first.
United States v. Wong Kim Ark, 169 U.S. 649 (1898)
At common law, with the nomenclature of which the framers of the Constitution were familiar, it was never doubted that all children, born in a country of parents who were its citizens, became themselves, upon their birth, citizens also. These were natives, or natural-born citizens, as distinguished from aliens or foreigners.
Perkins v. Elg, 307 U.S. 325 (1939),
Was a decision by the Supreme Court of the United States that a child born in the United States to naturalized parents on U.S. soil is a natural born citizen and that the child's natural born citizenship is not lost if the child is taken to and raised in the country of the parents' origin, provided that upon attaining the age of majority, the child elects to retain U.S. citizenship "and to return to the United States to assume its duties." Not only did the court rule that she did not lose her native born Citizenship but it upheld the lower courts decision that she is a "natural born Citizen of the United States" because she was born in the USA to two naturalized U.S. Citizens.
But the Secretary of State, according to the allegation of the bill of complaint, had refused to issue a passport to Miss Elg 'solely on the ground that she had lost her native born American citizenship.' The court below, properly recognizing the existence of an actual controversy with the defendants [307 U.S. 325, 350] (Aetna Life Ins. Co. v. Haworth, 300 U.S. 227 , 57 S.Ct. 461, 108 A.L.R. 1000), declared Miss Elg 'to be a natural born citizen of the United States' (99 F.2d 414) and we think that the decree should include the Secretary of State as well as the other defendants. The decree in that sense would in no way interfere with the exercise of the Secretary's discretion with respect to the issue of a passport but would simply preclude the denial of a passport on the sole ground that Miss Elg had lost her American citizenship."
The Supreme Court of the United States has never applied the term natural born citizen to any other category than those born in the country of parents who are citizens thereof.