Can my ex sue for back child support, when I was not notified that there was an order to pay child support.

If I understand the situation correctly, your daughter was living with you until she was 16 years old. Then the court switched primary physical custody to your ex without your knowledge. The order that was entered changing primary physical custody also awarded your ex some amount of child support. If that is the situation, there are a few exceptions, but generally your ex would be allowed to sue you for past due child support. The exceptions relate to how you were served and whether you should have been aware of the order. If you were not properly served or there is some other legal reason why you were not aware of the order, you may be able to set aside the child support (and/or custody order), making it as if the order was never entered. I would suggest you consult with an attorney to determine if you have any rights to set aside the order. There is a time limit to your ability to set aside an order, so it is best to contact an attorney sooner rather than later.

With regard to your ability to sue your ex for his/her failure to pay child support, you would be permitted to file a contempt charge against your ex for his/her failure to pay child support.