I'm 20 years old and don't talk to my father... he never took care of me can I put him on back child support

YOU as the child can't do anything... only your mother can... she would be entitled to what was owed up until you turned 18 (assuming she was actually awarded it by the court)... you however aren't.

No you can do no such thing. Has your mother passed away? Was child support owed to her? If there was never a order from the court then its over. No child support owed to anybody.

"Back" child support occurs when support is ordered by a court and not paid. So, if your father is in arrears on court ordered support, those arrears are collectible. But not by you. The arrears would be owed to the custodial parent, since support is paid to the custodial parent to help defray the costs of raising the child.

If there was no court ordered support then he doesn't owe anyone anything.

You also say he didn't talk care of you, are you sure about that? Are you sure that he didn't make support payments to your mother?