My 3 children, my husband, and myself have been living together for approximately 4 years, my oldest child does not belong to my husband and the donor that helped me conceive her has only met her a handful of times by his own doing. He has told everyone that I have denied visitation but that is not true. My husband would like to adopt my daughter and that is what she wants as well, but the bio dad will not allow it to happen to cause myself and my husband grief. However it is also causing my daughter grief. Do I have a case to have him deemed an abandoned father

Nope. If you had browsed around a bit before posting you might have found this sticky https://www.askmehelpdesk.com/family-law/child-abandonment-read-first-364259.html

Have you filed for child support from the father? That may be the only way to induce him to agree to the adoption.

Were you married at the time the child was born ?

As noted, who if any one is listed on the birth certificate ?
Is there a custody order in place ? Have you gotten a child support order ? Is there a child visitation plan in place.

But there is little chance of adoption if the bio father will not sign off giving his permission.