In the state of Florida, is there a statute of limitations for determining paternity if the child was placed for adoption at birth?

My adoption records werd released in 2005. I found my maternal family; my mother died in 2003. The physical description of my father matches her employer, who has been deceased since 1991. What are my options for determining paternity? I have located a grand cousin of my father and have contacted a dna lab to see if reconstructive dna could support my case. My "father" in question had no other known children. He was well-known and famous in his arena. During the conversation with the grand nephew, I mentioned dna and he seemed a bit resistant. He stated that since my alleged father had no children, his wealth was distributed amongst the family members and what makes him think I won't try and sue them for the inheritance. Considering he has been dead for 23 years, I wasn't sure if I were proven to be his child, would I have any rights of anything. I assured my cousin that my inital goals are to find my family, gain closure, and properly morn his death if he is indeed my father. Help?