I was born in Puerto Rico, As customary 60 years ago My uncle went to the city a month later he was asked to register me,
Well he registered me under his name and on the month that he we to the city. Now both my parents are dead, when they came to New York they registered me in school with their last name and on my correct day of birth, which I have lived my entire life with this identity. How do I fix this

Do you have a birth certificate? When your parents immigrated how did they identify you and register you?

Do you have a birth certificate? When your parents immigrated how did they identify you and register you?

Presumably, if OP does have a BC it corresponds to the information which the uncle registered in PR. I'm assuming that a BC was not required by the New York schools some half a century ago.

OP is not clear what he or she needs to fix, and why: the school records, the birth certificate (if there is one), or what and why?