paternity suit 
noun chiefly North American
A court case held to establish formally the identity of a child’s father.About a year after we married, my husband told me he was being sued in a paternity suit having to do with a one-night stand before we met....
- At various times he has been charged with assault and resisting arrest; he has been hit with a paternity suit.
- The driving incident came after the rapper went off in a courtroom in an earlier incident after being served with a paternity suit.