(CBS News) NEW YORK -- Dusten Brown has raised his biological daughter, 3-year-old Veronica, for the past year and a half. We met Veronica and Brown outside Tulsa, Okla., earlier this month.
"Everybody just needs to realize that she's happy. She's very happy here with us," Brown told us at the time.
Brown surrendered his parental rights before Veronica was born. Her unmarried biological mother then gave permission for her to be adopted by Matt and Melanie Capobianco.
The Capobiancos raised her for the first two years of her life, but Brown objected to the adoption. A Cherokee Indian, he cited a federal law protecting Native American children from being separated from their families and tribes.
"The only people that could really give you the - your history of your ancestors is your family," Brown said.
He was awarded custody in 2011, and Veronica was moved from the Capobiancos' home to live with Brown.
The custody fight continued all the way to the Supreme Court. In June, the high court ruled the 1978 Indian Child Welfare Act did not apply to Brown's situation.
Based on that, South Carolina's Supreme Court said last week that the adoption should go through, stating, "There is absolutely no need to compound any suffering that Baby Girl may experience through continued litigation."
Late today, Brown and the Cherokee Nation filed separate requests in South Carolina for new hearings in the case.
Watch: Elaine Quijano meets the father and daughter at the center of the custody battle, below.
Brown says Veronica doesn't recall who the Capobiancos are.
"She's seen pictures of them, you know, on TV holding her," he said. "She's just always like, 'Well, that's me, but who are they?' You know, I mean, it's sad that she doesn't know who they are, but to take her from us right now would devastate her, would ruin her world."
Veronica's adoption could be finalized in a matter of days. The Capobiancos have volunteered to go to Oklahoma to ease Veronica's transition. They say they're committed to making the transition sensitive and very gradual.