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If the time you need to recuperate and during which you will be receiving disability is 4-6 weeks, I would not suggest doing anything because the Court will accuse you of overloading the court's already heavy caseload and would most likely deny your Petition to Modify.
If it's more than that, file a Petition for Temporary Modification of Child Support" and tell the Judge when your surgery is, bring a letter from your doctor which should state an approximate recuperation time and ask the Judge to temporarily lower your child support amount during that time period. So that you will not have to go back to Court, ask the Judge to put a date in the Order as to when regular child support will begin.
The Judge will appreciate seeing you prepared with your doctor's report and will look favorably on your Petition when he sees that you are willing to resume regular payment of child support just as soon as you recuperate and are off disability
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ANDREA, JD, LLM
Member, NY & PA Bar