I would like a print out on my child's father support payment records

You can list them from your bank deposits history, or you can ask your child's father to send you a list of his payments (if he's keeping a record).

I'm guessing this probably doesn't answer what you are thinking...

What exactly is your question?

I suggest you do a Google search using the name of your state plus "child support enforcement" - it should lead you to contact info for your state's child support enforcement department.

How were the payments being made and were they through a child support agency ?

Yes, that is the issue, how are they made? Also you should be keeping a record of each payment.
Does he pay you direct? Or does he pay the state, who pays you?