Disclaimer: Not a legal expert.
Ex: Mathews v. Lucas, 427 U.S. 495 (1976)
The Plaintiffs argued that they were denied Social Security benefits because they were "illegitimate" children of their father even though the plaintiffs were able to prove that they were related.
The court held that among other reasons, because as defined in the Declaration of Independence that "all men are created equal", that there was no differentiation between a "legitimate" child and an "illegitimate" child in the eyes of the government.
There's a few other cases, but that's one that I've studied the most.