I think what you meant to say was that Congress does not have Constitutional authority to write legislation affecting the NATURAL BORN CITIZENSHIP status of a US citizen.
That is only partly true.
By the common law rule of citizenship that was in effect at the time the Constitution was adopted, Congress does not have authority to declare that persons born on US soil to either citizen parents, or to non-citizen resident parents are not natural born citizens, unless the child's non-citizen resident parents meet one of the very few limited historical exceptions.
In other words, if you were born on US soil, and your parents lived here, unless your parents were foreign royalty, foreign diplomats, or members of an invading foreign army, you are a natural born US citizen, and Congress has no power to declare otherwise.
Congress DOES have the Constitutional authority to state some conditions, however, under which you might LOSE your natural born citizenship.
In other words, Congress has the power to say that if you go and become a Cabinet member of the government of North Korea, you are no longer a US citizen (natural born or otherwise).
Congress ALSO has the Constitutional authority to determine the conditions by which a person born abroad is to be considered a citizen at or by birth, and therefore a "natural born citizen."
That Congress DOES have this power is clear first from the legal precedent in the common law. Parliament had previously possessed, and did possess at the time the Constitution was adopted, the similar power to declare which children born to English subjects abroad were also to be counted as natural born subjects.
That Congress has this Constitutional power is ALSO clear from the action of the First Congress, which (with President Washington) included 40% of the Signers of the Constitution.
They promptly passed a law declaring that the children born overseas to US citizen parents were also to be considered as "NATURAL BORN CITIZENS" (and therefore, eligible to be President).
If Congress had not possessed this power, in the judgment of 40% of the men who signed the Constitution, they would not have passed such a law.
Another string of letters arranged in the form of crap.