Adding My Father's Name on My Birth Certificate

My question involves paternity law for the State of: New Jersey

I am an adult. My mother did not put my father's name on my birth certificate because of welfare issues. This was in the 1980's. She is deceased now. My father and I have our names on Government records like the Veterans Administration, but I've always had my mother last name. My dad and I wanted to change it but know he is gravely ill and also lives in NC. I was told that in NJ that all I had to do was get a copy of my dad birth certificate, have a letter notirized stating what he wants done and send money for the correction. He was told that in NC as well. Now I called yesterday and they are saying paternity test. My dad can't take a paternity test because of his illness. And I don't understand why we have to so this since I'm an adult now. Can someone please help me or have any suggestions?

Well, it's pretty simple really.

Your birth certificate is a legal document. While we all know that Mom gave birth do you, we have no such guarantee about Dad. Or Bob. Or anybody else.

Now, can you please explain why illness prevents him from getting a cheek swab?

I have no idea why you were told that a copy of alleged Dad's birth certificate and a notarized document would be all you needed - that's not true for any of the 50 states (and there's a really good reason for that)

Worse still, NJ has a 5 year (after the child turns 18) statute of limitations on establishing paternity; there is one specific instance where it may be considered after the 5 year SOL, but you haven't mentioned anything about it.

The only other option I can think of is an adult adoption - but if that happens, your mother will no longer be considered to be your mother.