His suit seeks not only a paternity test but also drug testing of Smith and the infant, E! said.
If it is proven the child is his, Birkhead plans on seeking legal and physical custody, his attorney told E!.
Stern announced last week on CNN's "Larry King Live" that he was the father of the infant born Sept. 7 and he and Smith planned to be married.
Smith's son, Daniel, died in her hospital room three days after Dannielynn Hope was born and it was revealed he suffered a heart attack caused by a lethal combination of antidepressants and methadone.
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