Father rights

What rights does a father have if he didn’t sign the birth certificate and he isn’t involved in our kids life he goes months without seeing them or calling them in the past 2 years he’s only seen them handful of times for 30-40 min and doesn’t come again for another couple months I live in California he is on child support but he owes money and I receive 450 for my 2 kids thank you please comment he asks to take the kids but I don’t trust him and he’s threatening to take full custody