You'll need to file a downward modification petition to lower your support order. Depending on the reason for your incarceration, the court will probably lower your support order but the order WILL NOT terminate / be suspended while you are incarcerated.
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You can't dispute arrears. You can seek modification going forward - and should. Get a petition filed in Family Court ASAP.
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Sorry to be the killjoy, but incarceration is not a basis for a downward mod. Best bet is to see if supportive family could help pay your obligation as the children deserve to live in a manner "pre-problems." It is not their fault you cannot work and your poor judgment will not be rewarded legally.