I need advice on getting some type of legal rights and custody over my non-biological son

I was in a same-sex relationship with my x for over 10 years 2012-2022/23. She got pregnant. we had the baby in 2019, the hospital wouldn't let me put my name on birth certificate bc they said we didn't use a donor, so the father had rights and we weren't married. they refused to put me on birth certificate. so as of now by law I'm nothing to him. and she goes back and forth not letting me see him. i fully supported both of them, was the only one working from before he was born until we broke up in 22/23. I do have my name on his christening paperwork from the church, I'm on all his medical and school paperwork as the parent, i have tax paperwork claimed as my kid, plus a ton of pictures from throughout the years, friends and family who can all support that. He calls me mom that's all he ever known me as. now as of now she won't let me see him. I need help getting rights and custody.