The move comes even after the staffer, Bryan Pagliano, accepted an immunity deal with the FBI earlier this year and began cooperating
with their investigation into the server.
Pagliano was then subpoenaed by the conservative legal watchdog group Judicial Watch to testify as part of an ongoing Freedom of Information Act lawsuit they filed against the State Department. He is one of at least seven witnesses the group is interviewing over the coming weeks in that case.
In a court filing submitted Wednesday in that case, Pagliano's attorneys said their client is now "caught up in a lawsuit with an undisputed political agenda," and asked that the deposition, scheduled to take place on Monday, not be recorded.
Pagliano's attorneys added, "Mr. Pagliano will invoke his right under the Fifth Amendment and decline to testify at the deposition noticed for June 6, 2016."
"Asserting the Fifth Amendment in a civil procedure like this has its implications," Judicial Watch President Tom Fitton told CNN in response to the filing. "We're going to have to grapple with as best we can."
But the group is objecting to Pagliano's request not to be filmed, citing a decision by Judge Emmet Sullivan last week that ensured video from the depositions can't be released to the public
"Judge Sullivan already put a mechanism in place that addresses these concerns," said Fitton, adding that the video would be "helpful to Judge Sullivan in assessing the witness' demeanor."
Acknowledging Sullivan's order, Pagliano's lawyers said his particular deposition "presents not only privacy considerations, but unique constitutionally protected interests that require relief distinct from the (order)."
A State Department official declined to comment on the case, citing a policy not to address matters under litigation.
Pagliano, who was hired by the State Department after a stint as IT director for Clinton's 2008 presidential campaign, was paid separately by the Clintons to perform work on the server, located at their home in Chappaqua, New York.
He also pled the Fifth last year to avoid answering questions from the House Select Committee on Benghazi -- a congressional panel set up to investigate a 2012 attack on the U.S. consulate in Benghazi, Libya.