My daughters mother left us around 8 months ago and has not been back since. She is on drugs and has been arrested for this. My name is on her birth certificate as father but she was in another county when she delivered and I did not make it in time to sign it. She has not helped with any type of support for our daughter and I really don't want anything from her. She did file her federal taxes and claim our daughter even though she has not been around for 8 months or more.. how do I file something to keep her from just showing up and taking her from me when she abandoned her for over 8 months now?

If your child was left with a responsible person to care for her (YOU), its not abandonment, in the US anyway. Get awarded full custody through the courts.

Do you want a divorce, or legal separation? Either will suffice.

File with the court in your state for an award of child custody and support.

You do not file abandoment, you file for divorce. You file for custody of the child in court. The mother will have a chance to ask for visitation, but that will be a court issue.

You need to hire attorney and go to court for custody of child.