Illegitimate Child Financial Rights?

I live in FL, biological father lives in FL and mother lives in PA. I'm a secret illegitimate child born and conceived in NY. Only father, mother and I are aware of this. Biological father didn't financially support me or my mother. Biological father is very wealthy. I'm 35 years old. Do I have any rights to back child support or do I have rights to estate after death of father (79 years old)? Biological father will deny and fears his family finding out about me. Lastly do I have any rights to medical history? If the answer might be yes to any of my questions what process would have to take place to prove paternity?

Why have you waited so long? Likely, you are not entitled to child support, simply because you are no longer a child. If you are no named on a will, you likely are not entitled to his estate, either. As far as I know, though, you should be able to obtain a medical history.