Another ideological battle has broken out in the Education Department, this time over the choice to succeed fired undersecretary William C. Clohan Jr.

Gary L. Jones, a former Fairfax County school board member who is the current deputy undersecretary for policy and budget, is considered the front-runner, administration sources said. But they said internal foes had been trying to head off the nomination and had told the conservative journals Human Events and National Review that he is too liberal.

Secretary of Education Terrel H. Bell has said he expects Clohan's successor to be named shortly. The department's number two man was suddenly asked to resign last month without explanation. It was a period when Bell himself was under fire for not advocating forcefully enough President Reagan's plans to cut back the federal role in education.

The May 1 issue of Human Events said Jones would be an improvement over Clohan, but "is not wholly trusted by some conservatives" because he was an architect of the failed plan to turn the department into a sub-Cabinet foundation and reportedly has been critical of tuition tax credits.

The latest National Review said Jones "was once heard in public" opposing the tax credit plan, though he denied the charge. "But more importantly," it added, Jones "is not a movement conservative . . . . He is not likely to get out of bed in the morning thinking, 'How can I reduce the size of government today?'"

Linton Deck, superintendent of the Fairfax County schools, said Friday that he had written Human Events to say Jones did not argue against tuition tax credits at a conference last year, as the magazine reported.

"A Mr. Uzzell Larry Uzzell, a former aide to Sen. John East (R-N.C.), is now at the National Institute of Education was attacking the public school system, and Dr. Jones was one of several who corrected him," Deck said.

Jones is an advocate of tuition tax credits, he added. "I think his position is dead wrong, and I've tried to change his mind but failed."

Clohan, a former congressional aide, attributed his firing to pressure from the Reagan administration's right wing and outside conservative groups. He added that he felt the Education Department had "more than its share" of ultraconservative political appointees.

The 38-year-old Jones has made numerous public appearances explaining the administration's position on college aid and tax credits for students who attend private schools. He is generally considered by congressional aides and education lobbyists as a strong supporter of Reagan's educational philosophies, but not a rigid ideologue.

Charles B. Saunders Jr., chief lobbyist for the American Council on Education, a college umbrella group, said Friday that he considered Jones an "ardent defender of the administration's policies."

He and Jones have been carrying on an editorial-page debate about the effect of the president's proposed budget cuts in federal student aid programs.

Jones declined comment on the feud. Other sources said that some department officials with ultraconservative philosophies were trying to torpedo Jones' promotion.

"There's been a lot of infighting. You have to be ready to duck for cover on the way to the drinking fountain," one said.

Although Jones worked on the Reagan campaign and the transition team at Education, his conservative credentials are not as impeccable as some around him.

Bell's subordinates include general counsel Daniel Oliver, formerly of the National Review, whose headline on the Jones story was, "Will White House Sack Secretary Bell?"; acting deputy undersecretary for management Charles L. Heatherley, formerly of the Heritage Foundation, and regional office head Robert Billings, former executive director of the Moral Majority.

Just last month, the Conservative Digest, voice of the direct-mail expert Richard Viguerie, called for Bell's resignation because he had failed to stop grants and contracts to alleged leftist groups, including the American Bar Association.