If the non-custodial parent has not had contact with the child and has not paid child support for a significant period of time, then you can proceed with a Petition to Terminate the Parental Rights of the father in the Juvenile Court in the County in which the child resides.
I need some more information about the non-custodial parent and his current rights. Were the two of you married? Was the child ever legitimated? What are the Dad's current rights of visitation? Does he pay child support? How often does he see the child?
You could also pursue a Modification of Custody action to restrict Dad's visitation rights if you can prove to the Court that this would be in the best interest of the child. I urge you to speak to an attorney in a private consultation, so that he/she can learn more about your case and give you some advice and options on the best way to proceed.
Some law firms, like my own, offer free initial consultations. Please click on the link below and call us should you wish to schedule a free private initial consultation to further discuss your needs.
Please know that this is a general interest posting and does not create an attorney-client relationship.