Ex denied paternity of son. Did NOT want to meet son until he was 4 yrs old.Sporadic visits for 1 1/2 years. I filed to increase child support. Ex filed for full custody of son. Judge denied pending social study of both homes ( represented myself). Social study in process. Ex moved to Ga from Tx (3rd ex wife emailed me, she has 2 kids w/him-18 and 19 yrs) Have not heard from Ex for 1 yr. no calls,letters, emails. Do not know his address, just email address. Called legal aid. Backlog of cases. What can I do?

Ex denied paternity of son. Did NOT want to meet son until he was 4 yrs old.Sporadic visits for 1 1/2 years. I filed to increase child support. Ex filed for full custody of son. Judge denied pending social study of both homes ( represented myself). Social study in process. Ex moved to Ga from Tx (3rd ex wife emailed me, she has 2 kids w/him-18 and 19 yrs) Have not heard from Ex for 1 yr. no calls,letters, emails. Do not know his address, just email address. called legal aid. backlog of cases. What can I do?

Your post is very cluttered and all over the place so I'll try to answer this to the best of my ability. First, we'll need some questions answered:

Where are you located?
Where is the court case located?
What are your ex's grounds for requesting the custody change?
Does your ex have an attorney?

Your final question was, "What can I do?" What can you do about what? I'm not understanding what you're trying to accomplish. Are you trying to dismiss his motion for custody change? Then you would file a motion to dismiss his motion and the judge will either approve or deny it.

Agreed your post is not clear.

It sounds like the court action to increase support and change custody was first started over a year ago. Was the social study ever completed and submitted to the court?

I would submit a motion to the court to dismiss the custody action and rule on the support action. Once the support action is completed, you can try to get help from your local support collection agency to track him down.

... Do not know his address, just email address. ...

If a court case for custody and support is pending, and if the ex has appeared in that case, there will be an address on file for him. Anything you file in court can be sent to that address.

If the motions (your motion to increase child support and his motion for custody) are pending, and if you have filed the appropriate responses, there is nothing you need to do. If the court seems to have forgotten about it, you can request a hearing.

I tried to write a brief synopsis. I have primary care of my son. He has visitation rights-which he never exercised for did not meet his son until he was almost 5. Physical and court case location is TX. His grounds were that I was being investigated for neglect by CPS. I allowed my son to spend christmas holiday with him. A couple of days in to the holiday, CPS visited my home and informed me of allegation. I cooperated fully. CPS found allegation unfounded and closed case-in fact, the caseworker told me that they were not supposed to tell me who called in the complaint but she did anyway-it was him! He created that situation so that he could legally retain my son with him. He was to return son to me on a Friday. I got served on Monday. As I stated, Judge denied his motion pending a social study and ruled that my son was to be returned to me and he was. Social study was not completed because he moved out of State.It has been a year and we have not heard from him, which suits me just fine. I want this case to go away. I believe that me filing for an increase in child support motivated him to file for full custody for a kid that he has only seen a dozen times ( my son is now 8 years old)

OK, that makes it clearer, but doesn't change our answers.