CA can modify it and has jurisdiction now.
And child support goes on no matter what your job status currently is.
If you want to modify, hire a CA lawyer.
You now must litigate this case in California. You need to hire local counsel out there. CA is a large state, Where exactly did your ex move, and how do you go about seeing your child?
The other answers are wrong.
California and Illinois both have a law that determines which states rules in a case like yours. It's the SAME law -- word for word -- in both states. The law says that once a child support order is entered in Illinois, Illinois keeps "continuing exclusive, jurisdiction" :
Continuing, exclusive jurisdiction to modify child-support order.
(a) A tribunal of this State that has issued a support order consistent with the law of this State has and shall exercise continuing, exclusive jurisdiction to modify its child-support order if the order is the controlling order and:
(1) at the time of the filing of a request for
modification this State is the residence of the obligor, the individual obligee, or the child for whose benefit the support order is issued;
So, you might be able to write a letter to the court raising the CEJ argument . . .but the better practice would be to hire a lawyer in CA to knock the support case out of the CA court and bounce it over to the IL court.
Questions? Call -- 312-987-9999 -- no charge, no obligaiton.