Terdals

That's great! I think at this point it might be best to have a consult with a US immigration lawyer. The N-600K may not work for you anymore, but there may be some other less well known law that would apply to your situation and help you claim citizenship by birth. I think would definitely be worth the consult to see what they say. Sometimes even law schools offer consultation like services for immigration that may be helpful. Best of luck to you!

Are you still in touch with you mother's father? The one that lives in the US? If he is willing to help you out, or even if you can get a copy of his records to prove his citizenship, his residency in the USA and prove that he is your mother's father(such as with his birth certificate and your mother's birth certificate) then I'm pretty sure you can claim the citizenship. That second link that I included originally says in Part C, Item 3 that if a parent doesn't fill the physical residence requirement, the grandparent can. I don't think that it would matter that you are already an adult, but you would have inherited the citizenship upon birth and the USCIS application would just be getting that already inherited citizenship registered and recognized. But the only way to do it is with your grandpa's info and documents, so I hope that you are able to get them. If you have no way of getting ahold of your grandpa, it would be a lot more difficult getting everything you need to claim your US citizenship.

Initially I thought yes, you would be a citizen by birth, but after looking at the details closer, I don't think you are able to claim the citizenship unless you have contact with your grandfather. The parent has to have lived in the USA for a certain period of time as described below. So unless your mom lived in the US for at least 5 years, including a few years as a teenager, she is not able to pass on her citizenship to you. The USCIS page also talks about grandparent physical presence being sufficient. So if you can prove your grandfather's residence and citizenship in the US, and his connection to your mother and her citizenship, you may be able to claim the US citizenship. The law in effect at the time of birth determines whether someone born outside the United States to a U.S. citizen parent (or parents) is a U.S. citizen at birth. In general, these laws require that at least one parent was a U.S. citizen, and the U.S. citizen parent had lived in the United States for a period of time. A child’s U.S. citizen parent must meet the following physical presence requirements: The parent has been physically present in the United States or its outlying possessions for at least 5 years; and The parent met such physical presence for at least 2 years after he or she reached 14 years of age. https://www.uscis.gov/citizenship/learn-about-citizenship/i-am-the-child-of-a-us-citizen https://www.uscis.gov/policy-manual/volume-12-part-h-chapter-5#:~:text=A child's U.S. citizen parent must meet the following physical,reached 14 years of age.