I am a single parent to a one year old baby boy, the father failed to support my child and the last name of my child is mine, he refuse to acknowledge his name in my son's birth certificate.what can I do?

I don't know the law where you are. In the US you have to get the court to order the man to submit to a DNA test.

What do you want to do? Have you gone to court for child support? Has paternity been established?