I received a sum of money from my father when he passed. I used that money to pay off all of our bills. Now that we are divorcing we are paying bills off half and half. Am I entitled to my inheriatance back.

Not if the money is already spent. If you spent it - it's gone. The issue for you going forward is whether you can keep any remaining inheritance money from being split with your ex. If you have kept the inheritance in a separate account in your name only (not joint) and also separate from other moneys that are considered joint, then you should be able to keep all your remaining inheritance. But if the inheritance money is co-mingled with money in a joint account, or mingled in an account with other money that you obtained while married (for example from wages or investments) then it's almost impossible to unmingle them.

No, you are not entitled to reimbursement for money you spent, no matter what the source.

The exception (in NY) would be if you used it to purchase real estate. In that case, you'd be "entitled" to a larger share of the proceeds, depending on the division of your other assets.