I am 64 years old, just for medical reason I would like know, if individuals that are born in New York have to go through a legal process to find out if my real parent have suffered any medical problems, and if my children inherited the same?

Do you know anything about your adoption?

Adoption Information Registry - New York State Department of Health

Best place for you to start. You can get non-identifying information whether your birthparents have registered---and given your age, odds are that they haven't.

Getting your medical information is trickier. Your birth parents have to have registered for you to get that information. If you have a medical EMERGENCY that requires your genetic information, you can go to court to get the medical records of your birth parents---essentially, you'd be forcing open the adoption in this process. However, courts are extremely unlikely to open an adoption without a VERY good cause--like a life or death situation.

New York appears to also allow biological siblings to register, so it's possible you may be able to get more information than in other states, which could be lucky for you.

I would also register at adoption.org and ISRR to increase your odds of a reunion and getting medical information.

Good luck!