illegitimate
Used to describe that a child is not yours. Thus, making you immune to child support.

Can be traced back to as early as greek mythology.
Zeus or Posiden had a baby with Hoecles who had a son named Illegitimacus 

Since Hoecles cannot prove that Zeus or Posiden are the father, Illegitimacus is therefore Illegitimate, meaning none of them have to pay child support