In my moms divorce papers it states that 'no support shall be ordered to be paid, unless by further order of this court or a competent jurisdiction'. As an adult now, do I have rights to request back pay from my biological father, who never paid a dime?

Do adults have rights to request back pay child support

No, Child support is paid to the custodial parent for help in raising non adult children.

However, if you owe back support, the custodial parent can pursue it.

I see you posted twice, only the first one had more info. I merged the threads for you.

If your mother did not go after your father for support, then you can't do anything about it.