JUNEAU — Bills that would restore the portion of Alaskans’ oil wealth checks that were cut by Gov. Bill Walker last year were filed Monday, ahead of the start of the new legislative session.

The legislation to restore dividends was proposed by Republican Sen. Mike Dunleavy of Wasilla and incoming Republican Rep. David Eastman of Wasilla. Democratic Sen. Bill Wielechowski of Anchorage revived a proposal he has pushed previously with little success which he said would enshrine the current dividend formula in the state Constitution.

The Alaska Permanent Fund is a state nest egg of sorts born of oil wealth and grown through investments. The fund’s principal is constitutionally protected, but the fund’s earnings can be spent, if lawmakers choose. For years they’ve been reluctant to do so, for fear of being accused of raiding the fund. Dividends currently are drawn from fund earnings.

A major debate raging as Alaska struggles with a multibillion-dollar budget deficit is whether to use fund earnings to help pay for state government and change how dividends are calculated, as Walker has proposed.

Walker last year cut the dividend, citing legislative inaction on his plan to address the deficit, which also included tax measures. Wielechowski and others challenged his veto, but a judge found Walker acted within his authority. The case is being appealed.

In an interview last month, Dunleavy said people get “up in arms” when politicians meddle with the fund.

“It certainly impacts their dividend. But for a lot of folks that are conservative, the last thing they want is to give government access to billions of dollars to either maintain or grow government,” he said.

The bills to restore the permanent dividend funds were among more than 50 measures released Monday, with another round scheduled for release Friday. Monday’s batch included a bill that would provide survivor benefits for families of peace officers and firefighters, a version of which faltered last year.

Also proposed were bills that would let voters post selfies with their marked election ballots and bar state or municipal agencies from helping implement any federal directive to create registries based on race or religion.

Another bill would cut off legislative salaries and daily allowances if the Legislature does not pass a fully funded operating budget within the first 90 days of a session. Pay under the bill, proposed by Wielechowski, would resume once a budget passes.

While voters approved regular legislative sessions of 90 days, lawmakers in recent years have taken longer to finish their work. The constitution allows for regular sessions of up to 121 days, with an option to extend for up to 10 days.

“I think this would certainly put some pressure on legislators to get the job done,” Wielechowski said.

Incoming Republican state Rep. George Rauscher of Sutton has proposed putting a spending limit in the constitution. For any of the constitutional-change proposals to go before voters, they first will need two-thirds support in both the House and Senate.

Majority Senate Republicans will look at proposing some kind of spending limit in state law and the potential use of permanent fund earnings, incoming Senate President Pete Kelly said Monday.

The legislative session begins next Tuesday.