In context of who can be eligible to be president, there's nothing else to look at. Nothing newer has been enacted or modified. The most significant and relevant modification to citizenship law since the framing of the Constitution would be the 14th amendment, yet even after it was ratified, the Supreme Court still noted on two occasions that the definition of natural born citizen could only be found outside of the Constitution ... as in NOT within the 14th amendment.
Permit me to hint, whether it would be wise and seasonable to provide a strong check to the admission of Foreigners into the administration of our national Government; and to declare expressly that the Commander in Chief of the American Army shall not be given to nor devolve on, any but a natural born Citizen.- George Washington, Constitutional Convention, on July 25th, 1787