They say they later found out that only one of them was the infant's biological parent.
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Their lawsuit seeks damages from the Institute for Reproductive Medicine and Science for an alleged mistake of putting the wrong egg with the wrong sperm.
The Verona couple is suing the institute because their child is from another culture.
"It wasn't until the child was two years old that she started having, they're both Caucasian, she started developing Asian features," said the couple's attorney David Mazie.
The father had a DNA test and presented the results to the child's mother. According to court papers, the father told the mother, "it said zero probability of father".
The confusion and stress led to a divorce because of all the tension.
"She"s still their child, They love her. She's six years old now," said Mazie.
The non-biological father of the girl spends quality time with his daughter and has visitation rights, but is still waiting to tell her the truth.
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"At this point they don't think that she could fully understand that," said Mazie.
The parents want to find out who is the child's real father, and the six-year-old does have a blood disorder that they do not carry.
The mother called the institute to ask: "Could this be possible, could this really be possible?"
The dates in question are from November 2012.
"The court has now ordered that the clinic produce to us everybody of Asian descent who donated sperm, was inseminated during the critical times that family was there," said Mazie. "We want to find out who the genetic father is."
The institute released a statement saying: "This matter involves a private group in litigation. RWJBH does not comment on matters in litigation."