If he is actually her biological father, he does have the right to request that the Court adjudicate him as such and to ask for possession periods with your daughter. He would also have responsibilities, including child support, etc. Whether or not the Court would allow your daughter to live primarily with him, should be legally adjudicated as her father, would depend on the facts and circumstances of the case and the best interest of your daughter. If you anticipate that he is preparing to, or if he already has, filed a lawsuit, you should visit with a good family lawyer in your area to discuss the specifics of your case.
If your husband signed the birth certificate, then he may be the presumed father. (Whether he is the presumed father depends on some facts that you did not provide.)
If he is the presumed father AND he has represented to others that you are his child, then it may be too late for the biological father to interfere have have his paternity established.
Please consult with a local family law attorney who can ask you all the detailed questions necessary to help you determine whether the biological father has any right to bring a suit to establish his paternity and, if so, obtain possession and access rights.
If he can't bring the suit, then he can't obtain any rights. If he has no rights, your daughter has not ability to petition the court to let her go live with him.
What he is able to be appointed as a conservator of your daughter, despite her having a presumed father? Assuming you are providing a safe, stable home for her, a court is not likely to rip her out of your household after 11 years of no contact with her biological father.
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