The House Ways and Means Committee voted yesterday to stiffen President Carter's proposed "windfall profits" tax by extending to cover some Alaskan oil.

The amendment, which passed on a 22-14 vote, was widely regarded as a bargaining chip for negotiations with a conference committee when the bill passes the Senate. The Senate is expected to go along with the administration, which had exempted Alaskan oil entirely from its bill.

The committee also voted to ease the tax that Carter had proposed for so called "tertiary" oil - petroleum which must be flushed from the ground rather than merely pumped.

It also voted to exempt from the new windfall tax royalties from oil-producing operations owned by states which are used to finance public schools. The proposal applies primarily to Texas and Louisiana.

The series of votes came as the committee completed its secon day of work on Carter's proposal. The tertiary oil amendment was relatively minor. On Monday, the panel approved provisions that stiffened Carter's original bill.

The Alaskan oil amendment, sponsored by Rep. William M. Brodhead (D-Mich.) would extend a version of the windfall tax to Alaskan oil discovered before this year. The complex fomula, designed to encourage new exploration, would exempt newly discovered oil.

The proposal would impose an excise tax of 50 percent on produce revenues from Alaskan wells above a $7.50-a-barrel "base price" adjusted for inflation.

Staff estimates showed the proposal would increase the revenues gleaned by Carter's windfall tax by $1.2 billion over five years. The panel has estimated Carter's original measure would reap 20.6 billion over that period. The proposal involving tertiary oil, sponsored by Rep. Abner J. Mikva (D-Ill.), was designed to give oil companies an additional financial incentive to draw out hard-to-reach oil.The move would cut Carter's original revenue take by $500 million over five years.

In adopting the Mikva proposal, the committee rejected a plan by Rep. Jake Pickle (D-Tex.) that would have exempted from the tax all existing oil in fields where an oil company increased its prooduction of tertiary oil.