I went through the child support division. I receive no child support, but they are taking the father of my son to court over passport which is ky insurance. Since they have ordered him to do a paternity test and not the judge will he have any rights to my son?

First it is also "HIS" son, not just "YOUR" son. And he has always had rights, he just needs a court order to enforce them. The DNA test alone does not allow him to enforce any rights, but he can file in court for joint custody, visits or other levels of custody