First, you need to hire a family law attorney immediately. This is not something you should be handling as an uninformed individual. Even though the custodial parent receives public assistance, if they are not working and have no other reasonably identifiable source of income, they will have an income imputed to them, at least based on the minimum wage at 40 hrs/wk/month. If I understand your facts correctly, it sounds like the custodial parent wants you to possibly commit fraud re: what you allegedly pay her. Whether a judge possibly modifies the current child support order based in part on what the parties have done in the interim is going to largely be based on the facts, and how best that each side can argue them and convince the judge of such. Good luck.