Does a non-biological father have legal rights for custody after a divorce if he is not on the birth certificate?

Question Details:

My daughter was born before me and my ex-husband got married and he is not her biological father but has been there for her since 9 months of age. He is not on her birth certificate but was ordered to pay child support in the divorce decree. He now wants to fight for custody of her. Does he have any chance in getting it? He never legally adopted her either and does not have his last name. She has my maiden name and I'm the only one on her birth certificate.

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