Back Child Support/ Immigration Agreement

Me and my ex husband were divorced 8 years ago and child support was ordered, for which
he stayed current until about 2 years ago, he
got behind in the sum of $3,000.00. This past January he need me to sign a paper that
he was current on his child support so he could receive his citizenship approval, well
at first I refused then agreed upon him signing a paper stating that his was behind and that he agreed to start paying his court
ordered amount with him also repaying some
amount for the arrears. Well guess what here
it is 10 months later and he is current 0n his monthly but has not and says he will not
pay anything on the arrears. He claims since
I signed that paper he owes nothing. What can I do to try and collect what is owed to my child? And if I choose to take him to court what would happen? Doesn't he have to
prove to the courts that he did pay it? I am
willing to state that I only signed the paper
for his approval of citizenship and that it was not true. Please any advice would help.
We live in the state of California