I have been ordered to pay child support

I have been ordered to pay child support in the amount of $368.40 a month on 2 children that I am listed as the putative father of. I receive public assistance and after they get done taking child support I am left with less than enough money to pay my rent let alone my other bills. This order was placed because the children were in foster care. The judge has ordered permanent custody to someone else. What can I do to do away with this child support or at least decrease it to an amount I can afford?