This is from Wiki:
"Citizenship Clause
Main article: Citizenship Clause
There are varying interpretations of the original intent of Congress, based on statements made during the congressional debate over the amendment.[5] During the original debate over the amendment Senator Jacob M. Howard of Michigan—the author of the Citizenship Clause—described the clause as excluding American Indians who maintain their tribal ties, and “persons born in the United States who are foreigners, aliens, who belong to the families of ambassadors or foreign ministers.” He was supported by other senators, including Edgar Cowan, Reverdy Johnson, and Senate Judiciary Committee Chairman Lyman Trumbull.[6] Howard further stated the term jurisdiction meant "the same jurisdiction in extent and quality as applies to every citizen of the United States now"[6] and that the United States possessed a “full and complete jurisdiction” over the person described in the amendment.[7][8][6] Other senators, including Senator John Conness,[9] supported the amendment, believing citizenship should cover all children born in the United States.
In Elk v. Wilkins, 112 U.S. 94 (1884), the clause's meaning was tested regarding whether it meant that anyone born in the United States would be a citizen regardless of the parents' nationality. In that case, the Supreme Court held that the children of Native Americans were not citizens, despite the fact that they were born in the United States.
The meaning was tested again in the case of United States v. Wong Kim Ark, 169 U.S. 649 (1898) regarding children of non-citizen Chinese immigrants born in United States. The court ruled that the children were U.S. citizens.[10]
The difference between "legal" and "illegal" immigrants was not clear at the time of the decision of Wong Kim Ark.[11] According to The Heritage Foundation, which maintains that Congress possesses the power to exclude children born in the United States to illegal immigrant parents from U.S. citizenship by legislation, neither in that decision nor any subsequent case has the Supreme Court explicitly ruled on whether such children are entitled to birthright citizenship via the amendment,[12] although that has generally been assumed to be the case.[13] In some cases, the Court has implicitly assumed, or suggested in dicta, that such children are entitled to birthright citizenship: these include INS v. Rios-Pineda, 471 U.S. 444 (1985)[14] and Plyler v. Doe, 457 U.S. 202 (1982).[15]"
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So it would be nice if the Supreme Ct actually ruled on this.