Sadly, this is generally assumed based on a case from 1898… but birthright citizenship has never really been adequately tested by the courts.
>Most constitutional scholars agree that the 14th Amendment of the U.S. Constitution provides birthright citizenship even to those born in the United States to illegal immigrants.[24] As of 2015, there has been no Supreme Court decision that explicitly holds that persons born in the U.S. to undocumented immigrants are automatically afforded U.S. citizenship.[24][25][26][27][28][29][30] Edward Erler, writing for the Claremont Institute, said that since the Wong Kim Ark case dealt with someone whose parents were in the United States legally, it provides no valid basis under the 14th Amendment for the practice of granting citizenship to U.S.-born children of illegal immigrants. He goes on to argue that if governmental permission for parental entry is a necessary requirement for bestowal of birthright citizenship, then children of undocumented immigrants must surely be excluded from citizenship.[31]
>However, in Plyler v. Doe, 457 U.S. 202 (1982), a case involving educational entitlements for children in the United States unlawfully, Justice Brennan, writing for a five-to-four majority, held that such persons were subject to the jurisdiction of the United States and thus protected by its laws. In a footnote, he observed, "no plausible distinction with respect to Fourteenth Amendment 'jurisdiction' can be drawn between resident immigrants whose entry into the United States was lawful, and resident immigrants whose entry was unlawful."[28]
https://en.wikipedia.org/wiki/Anchor_baby