Snail darters and clean air claimed another victim yesterday at the Tennessee Valley Authority.

TVA Director William Jenkins, with three years left in his nine-year term, resigned yesterday after taking a final swipe at the three-dollar air cleanup program being forced on the agency by the Environmental Protection Agency.

In an announcement accompanying the unexpected one-sentence resignation delivered to the White House, Jenkins cited the dam-stopping fish and air cleanup controversies as the major "frustrations" imposed on the TVA board of directors by "external forces and other agencies" that have increasing control over the agency.

His announcement follows by a month the surprise resignation of the agency's top staff aide, general manager Lynn Seeber. Seeber gave no reason, but associates attributed it to his disdain for the outside controls that were being placed on the once free-wheeling agency by issues such as protecting endangered species like the snail darter.

Jenkins did not cite forthcoming Carter administration control of the board majority in his statement as a reason to quit, but he told a reporter in a conversation last week that major policy changes were "inevitable . . . I'm a hemmed steer in a field with new fence."

The 42-year-old Jenkins, a farmer, lawyer, and unsuccessful Republican gubernatorial candidate in Tennessee, had formed the two-member board majority with Chairman Aubrey Wagner that has resisted any compromise with the Department of the Interior that might save the natural habitat of the snail darter from the waters of the agency's Tellico dam. The dispute is before the Supreme Court.

And Wagner and Jenkins have steadfastly refused to sign a consent decree negotiated with EPA by new Carter board appointee S. David Freeman that would settle the nation's longest-running air cleanup battle.

Wagner's term will expire May 18, meaning that Freeman - a crusader for clean air who wants to negotiate with Interior Secretary Cecil D. Andrus to find a way to save both the Tellico Dam and the snail darters - will be the only board member until the White House fills the two vacancies. President Carter will be the first president since Eisenhower to name all three members, and only the third since President Roosevelt named the first board in 1933.

Carter, who has criticized TVA as "just another utility," has said he wants TVA, whose coal and nuclear plants far overshadow its hydroelectric dams, to become a national testing ground for solving the energy crisis. Appointee Freeman, for example, is a crusader for solar energy who says he wants to "hook TVA customers to the sun" and "make the valley the Detroit of electric vehicles."

Jenkins, appointed to the board by President Nixon in 1972, said he would have opposed the Tellico Dam - approved in the 1960s - because of the farmers it moved, but now believes the endangered species issue is not sufficient cause to junk the $116 million dam.

He said the EPA air controls, which would mandate cleanup of the poisonous sulfur dioxide from the agency's coal-fired steam plants, would cost $450 million a year and raise power rates to unacceptable levels for the poor and the elderly. The board majority has been unable to persuade either the courts or Congress that the air cleanup is unnecessary.

Agency attorneys said yesterday Freeman would be able to maintain programs, but would not be able to take any new initiatives until a vacancy is filled. A White House announcement of a nominee is not expected for several weeks.

While supporters of the Clinch River breeder reactor have expressed concern that Freeman would withdraw the agency's monetary commitment from that project, Freeman has said that while he opposes it "I would not pull the plug if Congress approves it over the President's veto." It is expected that the Senate will demand that the next two Carter appointees make a similar promise to support the breeder before they are confirmed.