Hello. This is a complex long question about US citizenship which is confusing, just saying in advance.
I was born in the mid 90's in Washington, DC to an accountant who worked at the Ukrainian embassy. He had diplomatic immunity, but according to him his immunity/paperwork or something along the line was different from the actual diplomats. He wasn't holding an actual diplomatic position and frankly the only reason he got hired there is because he is fluent in English, which was very rare in post-Soviet countries in the 90's. Since my father has a poor knowledge of law and stuff like that he doesn't remember/know what exactly he had and who he was exactly.
When I was born I was given a US birth certificate, which stated the Americanized version of my name (Andrew, real name Andriy) , they also gave me a social security number. When my father tried to get a US passport for me in DC he accidentally gave the people his diplomatic passport instead of his drivers license, so I was denied a passport and I'm assuming they have a record of that somewhere.
In 2003 my father was once again sent to America, this time on a proper diplomatic post. When we were obtaining visas my dad and mom(she is also Ukrainian) got one type of diplomatic visa (X1 with X being a letter that I don't know) and i got another (X2 or something like that) and the at the embassy they said that the only way for me to get the other visa was for my dad to sign a paper which would say that he wouldn't seek US citizenship for me, forfeit any claims for my citizenship or something in that tone. My father refused to sign the paper so i had the X2 visa. When in America I attended a US public school for 4 years, where my name in their records was Andrew. My father didn't attempt to do anything about my citizenship in this term. He was recalled in 2008. Since then there are no American documents about me and in all of my Ukrainian documents I am Andriy
Since then my father or I have not made any contact with US authorities about my citizenship and I have not traveled to the US. Now as far as I understand as long as I have a valid birth certificate and a social security number most US government institutions and private employers will say that I am a US citizen, however if I apply for a passport they will reject me (please correct me if I am wrong).
I wish to legally live in the US. I'm assuming that in most aspects I would be considered an American, however I wouldn't be able to get a passport. Is there any way to somehow be able to get a passport, like prove to them that technically my dad wasn't a diplomat or something like that? If not might I be eligible to obtain a green card or permanent residence just based on the fact that I was born there?
Thank you for your time and for reading. Any advice would be appreciated.

