My question involves a child custody case from the State of: California-Ohio

I have a 4 month old son no Paternity has been establish fathers name is NOT on Birth Certificate. There is however a Child Support case open through the state. I currently live in Ca and would like to Move to Ohio and Marry my fiance who will be adopting my son. Whats the best way to go about doing so WITHOUT being stuck in CA. Should I file in CA or in OH?