I live in Mississippi. I was co-owner to the bank safety deposit box which my father had at the time of his death. There was a will, which I am the executrix. There was some cash in the box, which I used to pay for the funeral. What are my responsibilities concerning the remaining cash? I have a "greedy" sister who insists it is hers.

What does the will state for distribution of property ?

That should tell you how to proceed. Treat it as if it were contained in an account. And disperse it per the instructions.

Your sister seems think that you used your portion of your inheritance to pay for his funeral, and so now she should inherit an equivalent amount for herself. That is incorrect. The funeral costs may be paid out of your father's estate assets (which includes his belongings in the safe deposit box), along with paying his debts and any costs for settling the estate, and then only after those expenses are paid for should you as executrix distribute the remaining assets to the heirs in accordance with the will. This assumes that the will doesn't have any specific instructions regarding what is to be done with the contents of the safe deposit box.