Will I have any say in a business contract that was between my father who is now deceased and his old business partner?

Are you receiving payments for yourself, or as the beneficiary of your father's estate?  If the former, you may have standing to enforce the contract or seek damages for its breach as a third party beneficiary of the contract between your father and his former partner; if the latter, the representative of your father's estate (the executor or administrator, or they may use a different term in NC) would be able to enforce the contract/seek damages for breach on behalf of the estate.  If no estate proceeding was instituted, starting one and getting an executor/administrator appointed would be a prerequisite to bringing any suit on behalf of hte estate.