D.B.
ETA - I see the confusion - you posted once, then responded to comments by posting a second question rather than editing the original. Members who want to see the whole story will need to read both posts, with this one second.
Original answer: I read your original question, and then unfortunately you "rephrased" it to take out so much relevant information. In the future, please add info but don't delete what was already there. On Mamapedia, we use abbreviations like "ETA" for Edited To Add or you can use the "So What Happened" feature.
As I recall, your original post said that you had given sole custody to your ex while you were not in a stable living situation. You were moving here and there, renting rooms, and you didn't think it was a good situation for your son. After a year, you became very stable and your ex gave you back your son, but there is still a legal document saying he has full custody. Now he has disappeared, you have tried to find him through various means such as social media, to no avail. But you located his stepfather who said your ex wants nothing to do with this situation without a DNA test. But you can't find him so how can you do a DNA test which you can't afford. Is that right?
Now you say you have been do court and they said they need an address so they can serve him with papers.
So, if you went to court on your own without legal representation or advice, you need to talk to a family law attorney. There are ways to get government assistance if you don't make enough to support your son on your own, first of all. Secondly, your ex is legally obligated to pay child support. My guess is that he is hiding to avoid all of that. But people are pretty easy to find either with the lawyer's paralegal doing a search or possibly using a private investigator for a few hours, which would be money well spent. You can file for child support through the enforcement division of your state - the lawyer can help you with this. Using your ex's social security number (if you know it) and other information, your ex can be found through his job if not through social media and other means, his wages garnished and paid directly to the enforcement division which will then get the money to you for your son. The court can order a DNA test if your ex protests this, and he has to pay support unless and until his paternity is disproven. He's going to have a hard time saying he's not the father if he took custody for a year and got an agreement for sole custody. That's pretty much admitting it's his son, right?
Get good legal advice.