A lot of people whom I argue with claim that Lynch v Clarke demonstrates that the basis of citizenship is English common law. Also, a lot of people quote James Madison's defense of William Smith as proof that we follow the English Common law on citizenship.
However, careful reading will show that this notion of following English Common law was just a habit in the absence of any knowledge of American law on whatever matter was before the court. As Madison himself said, if the State of South Carolina had a law decreeing who would be a citizen, it would have greatly simplified the matter. He is in fact saying, that a citizenship law of South Carolina would have decided the question, but in the absence of such a law, he turned to English Common law.
This is EXACTLY what the court said in Lynch v Clarke. Because New York did not have a law to determine who would be citizens of New York, the court decided to turn to English Common law. (They did not have to do so, they just chose to do so because that was their habit when dealing with any question before the court of which they knew of no governing law.) The New York State Legislature immediately responded to Lynch v Clarke by passing a law overturning the court's decision.
(All persons born in this state and domiciled within it except the children of transient aliens and of alien public ministers and consuls.)
That New York (and other states as well) could pass a law denying citizenship to the children of transient aliens demonstrates that English Common law was just a guide in the absence of positive American (or state) law. A place holder if you will.
I think this is the source of much confusion on the issue. English common law was the default position for those Judges who may have been unaware of the distinction between state and national citizenship, and the latter's foundation on natural law as described by Vattel.
As very few cases would revolve around the difference between state and national citizenship, it is easy to see how a correct understanding of the subject would be neglected in favor of more commonly applied law.