If I apply for MediCal will my partner be charged with child support?

I am pregnant and already have 1 child with my partner but we are not married. i tried applying for MediCal for me and my son but was told they would file child support on my partner since we technically aren't married. So i thought if I apply ONLY for myself and not my son maybe they wouldnt file child support. Please no rude comments! Thanks :)