What is the name of your state (only U.S. law)?
California
I was married for 35 years and my wife died. She was collecting SS benefits at the time. I have never paid into the system, only her, and I although born in New York, have no way of proving that I am an American Citizen. I need to know what steps I need to go through to get surviving spouse benefits. So far I have been denied any benefits from the SSA.
Why can't you prove you were born in New York? How old do you think you are and what do you base that on?
If you have proof that there is no birth certificate, then SSA will want secondary evidence. What does the original Social Security card application say? A microprint of that document can be requested. Did you go to school in New York? Were you listed on a census record in 1950? Did you get baptized or have another religious record of your birth? Where did you get married? What is listed on your marriage certficate as your place of birth? What is listed on your children's birth certificates as their father's place of birth? Have you ever voted in the United States? Do you have your brothers and sisters birth certificates? Where were they born? Where were your parents born? What documents are available to be reviewed? Who is your oldest relative and what evidence (in addition to their memory) can they supply?
Get as many old documents as you can. Hopefully they will all agree that you were born in New York. If they don't have the New York place of birth, maybe you weren't born in New York and you have been an illegal immigrant for the last 50, 60 years.
You don't say how old you are, but your US citizenship needs to be resolved now or as soon as possible. SSA is not going to change their mind about denying your claim without evidence. You don't want to be 80 years old and not able to get benefits. Maybe you should talk to an immigration lawyer. Maybe you need to get a Superior Court judge to issue a delayed birth certificate.
Get as many documents as possible. Get proof that there is no birth certificate. Get busy.