hello: I am familiar with a number of citizens who had children born abroad. Some of them born out of wedlock; others in bona fide marriage:
First case: If you are born to a US citizen parent ( one of the parents or both) in a foreign country, you became automatically citizen: if the child was born in marriage and if the parents report the birth and provide birth certificate with the consular of the country of birth. The consular staff find the paperwork credible, the child becomes a citizen and they issue passport.
The second case: whether your are born in wedlock or out of weddlock, at any point before 21 birthday, us citizens can claim their children, and DNA is the standard. If DNA stublishes parental relationship, then the child derives whatever status he/she is elligible.
For you to be born to US citizen abroad, showing up in the US without inspection and applying for a passport, that is a big leap. If the people who process your application issue a passport, you are lucky; if they discover that you are illegal here, you are in big trouble. It was in my opinion a wishful thinking to do that. Also claiming to be a US citizen is big trouble in itself....We will see what happens...