It may not be the best title for a fiscally conservative Republican, but Alaska Lt. Gov. Terry Miller can justifiably claim to be the son of Santa Claus.

And fittingly enough, he is running for governor at a time when the state has a bag full of goodies to give out, even though no one can agree how to do it.

Miller's father, Con Miller, was for years mayor of North Pole, Alaska, running a "Santa Claus House" store which thrived from tourists here to make use of the town's unique postmark. The elder Miller often dressed up as Kris Kringle.

By age 20, Terry Miller had been elected to the North Pole City Council and then to the local borough assembly.

He moved on to the state House of Representatives in Juneau, the state Senate, and then the lieutenant governorship, becoming today an articulate and thoughtful 39-year-old with more experience in state government than any other Alaskan of his generation.

But in an increasingly rough primary in this traditionally rough state, even with a 2-to-1 lead in some polls over former state senator Tom Fink, Miller's supporters are beginning to wonder if their candidate may prove to be too smooth and too familiar for Alaskans.

"Terry Miller has been a professional politician since he was 20," said one of his opponent's campaign consultants. "He has never had full-time, permanent employment."

Whether that tactic will work is unclear. "We'll find out," said Miller.

For now, the fight is over what to do with an oil revenue "permanent fund," now about $4 billion, most of which under current state law must be paid back to state residents.

Few candidates running for state-wide office in the Tuesday primary say they are satisfied with this year's giveaway of $1,000 checks from the fund to every man, woman and child in the state.

Miller favors junking the cash giveaway and starting a pension fund instead. This would help Alaskans avoid income taxes on the money and at the same time make them seem less greedy to other Americans, particularly those in Washington who have submitted bills limiting the state's ability to tax oil revenues.

Fink, an Anchorage insurance agent with 11 children, wants to set up a fund for low-interest loans to help more young Alaskan families buy houses.

A balding man who favors bow ties and cannot match Miller's accomplished speaking style, Fink has managed to build up considerable support by calling for regular use of the death penalty.

Miller opposes the death penalty as ineffective and immoral but has tried to counter Fink by calling for mandatory sentences with no parole for first offenders in violent crimes.

Miller opposes moving the state capital from Juneau in the far southeast, earning him heavy support from Alaskans in the Juneau area who are fighting a November ballot proposition that would mandate the move.

Fink strongly favors building a new capital in the small town of Willow, not far from Anchorage -- the area where about half of the state's voters live.

Fink also supports a ballot initiative that would end special preference in hunting game and fish for natives and other Alaskans who live off the land, an emotional and racially tinged proposal that Miller and the two leading Democrats in the governor's race oppose.

Alaska has an open primary, which means Miller could collect the votes of some Democrats and less conservative independents.

Miller said in an interview in this second largest city of Alaska, 14 miles from his North Pole home, that Fink's "people vote for sure and my people vote depending on whether they have an extra summer job that keeps them away from the polls or not."

Fink, 54 this month, is expected to spend about $500,000 to Miller's $700,000.

If Fink loses the primary, many politicians here believe, he may desert the Republican ticket and endorse a Libertarian, state representative and fellow insurance agent Dick Randolph, for governor.

Randolph, 46, is not in the primary because the Libertarian Party here, despite a 12 percent showing in the 1980 presidential race, is not yet an official state party. It cannot become so until it polls 10 percent in a state government election.

Randolph, interviewed as he sipped a 7-Up at the Tanana Valley Fair here, predicted he would meet that goal easily. With Fink behind him, he suggested, he might even draw enough support from conservative Republicans and Democrats to win the general election.

The Democratic side of the race has generated less interest, with hotel magnate Bill Sheffield getting a lead by starting early and building up a $1 million campaign chest.

Steve Cowper (pronounced Cooper), a quiet, thoughtful but under-financed former state representative, is trying to catch up.

Sheffield, 54, wants to use the permanent fund to provide low-cost housing loans as well as to improve roads, build power projects and make other permanent improvements from which the state can profit even after the oil runs out.

Cowper, 44 this month, suggests the fund should be preserved for those days when oil revenues run out.

A poll of 1,279 Alaskans done in early June for the Cowper campaign showed Miller with 26.6 percent, Fink with 14 percent, Sheffield with 14.7 percent and Cowper with 13.5 percent.

But Alaskan elections have always been difficult to predict and hair-thin victories have been common