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Actually, it may be possible for the 'possibly real' dad to come forward and file a petition with the Court asking for a paternity test based on his testimony/affidavit that you two were intimate at a time when science says the child was likely conceived and that he now has reason to believe that he is the father. He can use an affidavit by you where you state under oath that you had relations on or around XX date, and that you learned you were X weeks pregnant on or around YY date, which was X number of days after you started having relations with Timmy. Once he is granted the right of a paternity test he can prove parentage and seek custody and/or visitation. It may NOT negate Timmy's right to visitation or even custody if he fights for it and the court finds it in the child's best interest, particularly if they find Timmy to be "in loco parentis" to the child - the only father the child has known. But, it can get the other dad some rights. As for your rights, you need to make those motions to enforce the child's right (and yours) to a relationship with you - your visitation rights, etc.
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