If your ex-spouse is receiving Social Security Disability (SSD) benefits, it is usually because they can no longer work due to their disability. The benefits are supposed to compensate for the pay that would have been made by your ex, had they not lost the ability to work.
The children of these disabled workers are entitled to something called SSD Dependency benefits, which are used to help take care of the child’s needs. If you are unable to work, and therefore make income, you are not the only one that suffers, so the Dependency benefits are there for the children.
However, being disabled does not excuse you from paying court-ordered child support, and the court is very certain on making sure that the children do not suffer because one of their parents is on disability. The court will usually allow the payer to use their Dependency benefit payments as part, or all, of their monthly payments. In other words, you can use some of your disability benefits to cover child support, and then fill in the remaining gap of what you owe with the Dependency benefit payments.
Note that if your spouse receives Supplemental Security Income (SSI), you will not be able to get any support payments from that. If your ex is collecting and owes support, the court or a Social Security officer can cut into those benefits, in order to put pressure on your ex spouse to make the appropriate payments.