Hi - my name is XXXXX XXXXX X'X a Family Law litigation attorney. Thanks for your question.
Child support is based mainly on your income, along with other relevant factors. Because child support is set by statute, there's not a lot of grey area when it comes to pay support.
Thus, you cannot sue to stop your support amount from being changed. However, you do have the right to only be required what the law says you must. The amount of support you should be paying can be calculated here: http://www.childsupportillinois.com/general/calculating.html or here:
It may be that you're paying more than you are supposed to already. In that case, you could ask the court to reduce your obligation.
As for claiming the child on taxes, that's usually dealt with in the child custody order. If you're not set up to be able to claim the child, you certainly can file a motion to modify the order and ask the judge to allow you to claim the child every other year, etc.
she also moved my child out of state without my permission, can i do anything about that?
If the court order says that she cannot move out of state without your approval or the court's permission, and she did so anyway, you would have the right to file a motion to hold her in contempt of court and also ask the court to order her to return the child.
Most court orders do provide that the court must approve a move, so you should take a look at that.
If there is no such provision, you can still file a motion to modify the current custody order based on the fact that the child lives so far away that you cannot reasonably exercise visitation with the child. You can then ask the judge to change the order to allow you reasonable visitaiton.
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