Who Am I and How Can I Prove It?

I have a very rare medical disorder and it is hereditary. They need more information from my fathers dna. This is the problem he is dead and he was never placed on my birth certificate for me to gain access to his medical records. What can I do to prove I am his daughter. He also never paid child support or had me in any wills or paperwork. But I am his daughter. How Can I get DNA?