Do I need to prove paternity to get inheritance from my fathers estate?

I am sorry for your loss.  And for the trouble besides.  First, did your Father leave a Will?  If he did and you are in it as his son then my feeling is that if he did not question your paternity neither can anyone else to disinherit you. 

However, if he died without a Will - intestate - then the intestacy laws of the state will govern and the issue of paternity will be at the forefront.   Establishing paternity has become easier with the advancement of science in the field of DNA.  But that is not the only way it is established.   There are three main ways in which paternity is typically established; by a paternity affidavit, by an administrative order based on genetic test results, or by a court order.  Proving paternity without DNA evidence is recognized in most states.  The fact that your Father held you out to be his son in an open manner is a plus.  You would need to contact an attorney in your area and discuss the matter in detail should this be an issue that needs to e resolved before you are to receive your inheritance.  Good luck.