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Good afternoon. If it is determined that you are the father, you would have a right to seek custody of the child or visitation, depending on how involved you want to be. Moreover, there would be a legal obligation to pay child support, so she could go after you for it as well. Seeing how the child turned 3 and you have not been involved in their life over all this time, visitation may be something more likely to be ordered at this time, rather then any type of shared custody. Of course, unless and until a test is ordered by the Judge, you do not need to voluntarily submit to this and can sit idle and wait to see if she takes action, if you desire.
I just wanted to follow up and see if you had any other questions or needed me to clarify something. I am here to help, so please let me know. Thanks!