Larry Birkhead was revealed as the father by DNA tests this month. He and other participants in a private custody hearing Wednesday said they could not discuss the proceedings, but Birkhead said he was pleased.
"I guess all I can say really is that it was a good day for me in court," he said.
Virgie Arthur, the mother of the dead reality TV star, has been trying to reach a visitation agreement that would end her legal challenge for custody of the baby.
After the Supreme Court hearing, Arthur was served with a lawsuit, Entertainmnent Tonight reports. Sources tell ET she's being sued by her former Bahamian lawyer for non-payment of fees.
Arthur left in a taxi without speaking to reporters.
The judge scheduled another hearing for June 8.
Birkhead, a 34-year-old Los Angeles photographer, said efforts were "in the works" to obtain a passport for Dannielynn and change her birth certificate to remove the name of Howard K. Stern, Smith's last companion. He said he hoped to leave the Bahamas for the United States with her "pretty soon."
"I just want Dannielynn to have a good life," Stern said.
The girl could inherit a fortune if lawyers resolve challenges over her mother's estate in her favor. When she died of an accidental drug overdose in a Florida hotel room, lawyers were still wrangling over the estate of Smith's late husband, the Texas oil tycoon J. Howard Marshall II, estimated to be worth more than $1 billion.
Smith gave birth to Dannielynn in September only days before her 20-year-old son Daniel died of a drug overdose at her bedside.