You will need to first file a Paternity Action (not a paternity test) to establish you as the father and address custody, visitation and support for the child. The actual petition is called 'petition to establish parental relationship'. The fact that you are on the birth certificate does not mean that you are legally the father as you must file this petition in the Family Court to establish this.
Once filed, the mom would need to be served. In court, you will either agree on a visitation schedule or the judge will make a determination. Custody & support will also be addressed.
Answered on Oct 01st, 2014 at 2:04 PM