The filing states that Hunter Biden "was not expected to challenge the results of the DNA test or the testing process."
Hunter Biden denied in a previous court claiming to be the child's father, but agreed in October to a paternity test.
Neither Joe Biden's campaign nor an attorney for Hunter Biden responded immediately to requests for comment.
This is the latest development to push the son of the former vice-president to the spotlight as Joe Biden seeks the Democratic 2020 presidential nomination. The news came just hours before 10 Democratic contenders gathered in Atlanta for a debate.
Lunden Alexis Roberts, 28, filed a lawsuit in May seeking child support and childcare, born in August 2018. The latest filing by his lawyers also records that members of Biden's family are eligible for Secret Service protection.
In a filing on Wednesday, Roberts asked the court to seal the name and identifying information of the child in anticipation of the court granting a birth order as a result of a review of the DNA.