Originally Published: 01 MAY 23 12:29 ET

Updated: 01 MAY 23 13:49 ET

By Marshall Cohen

(CNN) -- An Arkansas judge on Monday ordered President Joe Biden's son, Hunter Biden, to answer additional written questions about his investments, his art sales and other financial transactions as part of a paternity-related case.

Hunter Biden also will sit for a deposition in mid-June, where he'll have to answer questions under oath, the judge said.

Independence County Circuit Judge Holly Meyer also chided Hunter Biden's lawyers for overly redacting their filings and hiding information that should be public.

"The ability to redact is being somewhat abused," Meyer said, ordering lawyers to re-file public versions of some of their previous filings, including some that had been "sealed" and fully blocked from public view.

The filings likely included information about which financial records Hunter Biden might need to turn over to Lunden Roberts, an Arkansas woman who is the mother of one of his children.

Monday's hearing in the years-old case comes after Roberts, the mother of one of his children, asked an Arkansas judge to hold him in contempt -- and send him to jail. She claims he is ignoring court orders requiring him to turn over documents about his finances.

The case was reopened in September when Hunter Biden asked the judge to reduce his child support payments. He told the court that there had been "a substantial material change in (his) financial circumstances" since the 2020 settlement, alluding to a sizable drop in his income.

This gave Roberts an opportunity to reopen the "discovery" process and demand records about Hunter Biden's finances. She requested information about his art sales, an inventory of his properties and cars, details about his travel habits, and records about his tax difficulties.

Paying $20,000 monthly in child support

Hunter Biden is paying $20,000 a month and has paid $750,000 so far to Roberts, his lawyer said on Monday, publicly revealing the figure for the first time.

A trial is slated for July to determine if his child support payments will be adjusted.

The case is playing out while House Republicans are similarly pursuing many of Hunter Biden's financial records, including many of the same ones that Roberts wants.

Hunter Biden's lawyer, Abbe Lowell, complained at the court hearing Monday about alleged leaks to the press. Lowell, a high-profile DC defense attorney who is now representing Hunter Biden on several fronts, said the press stories were creating the false impression that he is a "deadbeat dad."

It's important to "let the world know" that Hunter Biden is keeping his word and paying his child support, Lowell said. "He is paying what he agreed to."

Lowell also suggested that people tied to Roberts may be giving the press sensitive information that they obtained as part of the legal case. Roberts' attorneys denied those allegations Monday in court.

Meyer agreed that there was "suspicion" of possible leaks but said Lowell hadn't provided enough proof.

"I have been very generous to Mr. Biden," in terms of keeping sensitive information under seal as part of the court record, Meyer said. "But I can't gag the whole world."

This story has been updated with additional details.