My child, now 3 years old, was born in VA. Her father's name is on her birth certificate, he kept in touch with her until she was 4 months old, then we moved out of the country. While still there he did not help financially, but did pay for her health insurance for those 4 months.
Over the last 3 years since we moved, he barely kept in touch with her. Months can pass without him calling or emailing. He is manic-depressive and an alcoholic (trying to quit but not making any real effort for that... ). Not financial help or emotional support.
I will say I know he thinks of her a lot and loves her, but... That's not enough for a child. His life is a mess and he is uncapable of taking care of another being since I have knows him, and sadly enough I don't know if this will ever change.
I have sole custody of the child, but was wondering if there's a way to terminate his paternal rights...

No...

Only a court can do that... and usually only if the child's safety is at risk. And it isn't.

And the few cases it is... an adoption is usually part of it.

Take the time to read this sticky...

https://www.askmehelpdesk.com/family-law/signing-over-rights-read-first-116098.html

Yeah you'll have to talk to a lawyer.. and find out what that states law is I'm kind of in the process of the same thing except my child's father hasn't had contact for 10 yrs and I'd like for my husband to adopt her