Hunter Biden is the "biological and legal father" of Baby Doe, the child of an Independence County woman, Circuit Judge Holly Meyer declared in an order signed Tuesday.
DNA results showed "with near scientific certainty" that he fathered the child, she stated in an "Order Establishing Paternity."
The judge also ordered the Arkansas Department of Health to issue a "new or substituted" birth certificate listing Robert Hunter Biden as the father and Lunden Alexis Roberts as the mother of the child, born in August 2018.
Biden is the son of former Vice President Joe Biden, the highest-polling Democratic presidential candidate.
The toddler, initially referred to as "Baby Doe," will henceforth be referred to in court documents by his or her initials: NJR. The court had previously ruled that the child's actual name would be sealed.
In a separate order, the judge awarded "primary physical and legal custody" of the child to Roberts.
As the non-custodial parent, Biden "shall have visitation with the child as agreed between the parties," Meyer wrote in the separate "Order on Custody and Visitation," which also was signed and filed Tuesday afternoon.
In addition to paternity and custody orders, Meyer issued a supplemental protective order, preventing the release of the parties' financial details.
In the "Supplemental Protective Order," Meyer ruled that "there is good cause for the protection of private information of the parties" and that "it would not be in the parties or the child's interest to divulge the confidential financial information of the parties."
Failure to seal information about the parties' finances would further delay the case, which was filed more than seven months ago.
If either side finds it necessary to unseal the information, they must petition the court for a hearing prior to divulging it.
Biden's attorney had asked the court to limit the scope of depositions, but Meyer declined to issue a detailed order to that effect. She emphasized, however, that child support is the only unresolved issue.
"[A]nything germane to child support may be inquired into in discovery and not those matters unrelated to child support," she wrote.
While allowing depositions to proceed, she limited the number of people who can attend or have access to what is said: Only Roberts, Biden, their attorneys and a court reporter/videographer can witness the session.
Those depositions will then be sealed, she noted.
Financial data and other confidential information can be shared with expert witnesses who are retained by either side. But they must first acknowledge in writing that they are aware of and bound by the protective order. They'll also be informed of the potential penalties for those who fail to comply; including fines, incarceration and other sanctions.
The order, which bore the judge's signature, was also signed by Roberts' attorney, Clinton Lancaster, and Biden's attorney, Brent M. Langdon.
Langdon's office didn't respond to a request for comment Tuesday. The Texarkana, Texas, attorney doesn't comment on pending litigation, his office has said.
Roberts, 28, filed the paternity suit against Biden in May, seeking a determination of paternity as well as child support. After initially denying the existence of a previous sexual relationship, Biden, 49, eventually agreed to take the paternity test.
Roberts alleged in a court filing that Biden hadn't paid child support in more than a year.
Biden denied the allegation in a motion and brief earlier this week.
Questions about Hunter Biden's finances, employment history and previous substance abuse have been raised by Republicans during the impeachment inquiry into President Donald Trump.
Republicans have criticized Hunter Biden's business dealings in Ukraine and China, questioning the sums he received from companies in Ukraine and China.
Biden and his father have denied any wrongdoing, portraying the attacks as baseless and politically motivated.
Hunter Biden served five years on the board of Burisma, a Ukrainian natural gas company, but left the position in April, the same month that his father entered the presidential race.
Hunter Biden told the court in a signed Nov. 27 affidavit that he is unemployed and hasn't had a monthly income since May.
Roberts alleges that Biden is concealing information about his income and assets and has failed to turn over financial information as required.
Thus far, Biden, who resides in California, hasn't appeared in court for the proceedings.
But Meyer is requiring him to appear at all future hearings unless he gets excused in advance, Lancaster said.
Those have been scheduled for Jan. 29 and March 13. The third and final hearing is on the docket for May 13.
Roberts is pleased that her case is advancing, Lancaster said Tuesday.
"She's ready to get some child support going in this situation," he said.