Per your question, I am assuming that a child support order has been entered whereby your child's father is under a court order to provide support for your child. With that said, if he wanted to reduce or abate his child support obligation, he (not you) must file the motion. Moreover, should he file the motion, he must show the judge that a modification or abatement is justified since there has been a "change in circumstances" (i.e. he is locked up); however, please know that the judge shall ultimately consider all the factors and make a decision. Furthermore, the fact that a person paid support when he "did have money" has no effect on the motion to modify or abate.
if HE wants to modify his support obligation, HE (not you) must do so.
if you are receiving any public aid including link or all kids medical, then the support is not yours to decrease, it belongs to the state.
take all your child support papers to a lawyer for a consultation.