I am a single mother of a two year old and The daddy has nothing to do with him because he doesn't believe that my son is his. He doesn't want to get a DNA test and I filed for child support but I believe he is running because I haven't heard from them for about a year and a half and he has moved and change his number and he has such a common name its hard to find him. Someone told me to take him for child abandonment because he could be running for a while what do I do and how do I file

In my view you have to settle first the question about paternity and child support .Get a lawyer and do it.
You were told wrong... You cannot take him for child abandonment if he has never been your child's legal father.