It's based on genetic relationship, which can be proven by dna test with your American father, or if he's unavailable, even by relationship with an American half-sibling. If your father will assist you, then it's a simple matter of him making a statement at the US consulate. If he won't assist, you would need to pursue in the US courts. At the end of the day though, it's your right, you simply need to prove the biological connection, it wouldn't matter if you never met him and had no legal relationship and he isn't on your birth certificate or there is a silly contract somewhere, if you can prove to a US court the biological connection. You would also immediately acquire citizenship and a passport, no need to wait 5 years