Washington (CNN) Another one of Roger Stone's former aides has been subpoenaed to turn over documents and appear before the grand jury in special counsel Robert Mueller's Russia investigation -- an effort his lawyers are aiming to beat back in court.

"I'm actually on my way to the courthouse to file the motion to quash the subpoena on the grounds that special counsel Mueller's appointment by Deputy Attorney General Rod Rosenstein is unconstitutional," said Paul Kamenar, a lawyer for Andrew Miller, the former Stone aide.

A number of current and former associates of Stone -- a longtime adviser to President Donald Trump -- have been contacted or received subpoenas from the special counsel in recent months, as Mueller's team appears to ramp up its investigation into Stone

Stone has said he has not been contacted by Mueller's team

Miller performed assorted tasks for Stone over the years, including maintaining emails for various Stone-related websites. Another one of his lawyers, Alicia Dearn, said Miller has had only limited contact with Stone since 2014.

During the 2016 election cycle, the super PAC founded by Stone shelled out $9,000 to A Miller Research -- a business run by Miller -- for consulting, according to the Center for Responsive Politics. He helped Stone coordinate appearances and media interviews during that time and was paid through the super PAC, Dearn said.

Stone insisted Miller did only minimal work for him for the 2016 campaign.

"Andrew Miller has not worked for me for three years," Stone said. "He did not work for me during the 2016 campaign, although he did fly in for the Republican National Convention to work on my scheduling."

When asked about the thousands of dollars Miller was paid by Stone's super PAC, Stone said, "I believe he did some IT work."

Miller had been battling with the government over what he and his lawyers believed to be an overly broad document request. Eventually, they handed over some documents to Mueller's team.

After handing over a set of documents, Miller received subpoenas for additional documents and testimony before the grand jury, Dearn said.

Dearn said, after poring over tens of thousands of emails, Miller's team has not found anything that appeared particularly relevant to the Russia investigation. She said she does not believe her client is a target in the investigation. Miller initially wanted to cooperate with the special counsel's inquiries but after what Dearn called prosecutors' "heavy-handed" approach, she said they are now looking to challenge Mueller's authority.

"We should all be concerned when an unchecked prosecutorial power starts threatening ordinary citizens," Dearn said.

As Miller's attorneys say they will try to shift the battle to a fight on constitutional grounds, they are testing an argument that other defendants in the Mueller investigation have been trying out as well. Their court filing to fight the subpoena was not yet available Thursday afternoon.

Two defendants in criminal cases brought by Mueller, former Trump campaign chairman Paul Manafort and the Russian company Concord Management and Consulting, have tried to argue that Mueller lacks prosecutorial authority.

Manafort's argument that Mueller went outside the lines of his appointment to charge him was shot down twice by federal judges in both DC and Virginia.

While Concord Management and Consulting hasn't heard the court's response yet to its constitutional challenge of Mueller, federal Judge TS Ellis wrote in an opinion earlier this week that Mueller certainly had the constitutional authority to bring a case because he worked under Department of Justice leadership. "it is worth noting that such an objection would likely fail," Ellis wrote. "He is required to report to and is directed by the Deputy Attorney General."

Kamenar is representing Miller at the request of a conservative nonprofit, the National Legal and Policy Center, which is paying his legal fees.

"We were anxious to force the constitutional issue and we're hopeful that we can do that through Andrew Miller," said Peter Flaherty, chairman and CEO of the National Legal and Policy Center. "We're hoping we can advance this up the judicial food chain and get a ruling."

Miller, who currently works as a house painter in St. Louis, has said he has little to offer the Mueller team, according to Flaherty.

"Andrew's an interesting guy. He was not a Trump supporter. He's a supporter of Libertarian candidates," Flaherty added. "He's also just an ordinary guy. He's very much at the edge of this thing, yet he's been sucked into Mueller's very broad probe."

Kamenar said he is not sure what Mueller's team is interested in gleaning from his client.

"I have no idea," Kamenar said. "They're basically doing what appears to be fishing expeditions for some of these collateral witnesses."