While you have your child living with you, you need to go file a petitoin for temporary custody explaining in the petition that the child is currently living with you, that the mother has no place to live, and has asked you to keep the child in your home.
You need to also file a Petition for custody as well as a motion to quash child support. If you don't file a Motion to quash child support, you will still have to continue paying the child support to your ex-wife so as to avoid being in contempt.
I would highly suggest getting these documents filed quickly as most Judges are more likely to order temporary custody if the change will not upset the child. The fact that your son is with you should help in getting this granted.
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