PHOENIX — An Arizona lawmaker endorsed by former President Donald Trump who attended the Jan. 6, 2021, rally that preceded the violent assault on the U.S. Capitol and another lawmaker who also believes the 2020 presidential election results should be overturned are among four Republicans vying for the top elections post in the presidential battleground.

It’s a trend seen in several Republican primaries this year that has led to mixed results for those who peddle conspiracy theories and promote the falsehood that widespread fraud led to Trump’s defeat. Tuesday’s primary elections feature similar candidates in Kansas and Washington state.

In Kansas, voters will choose between a challenger who questions the 2020 presidential results and the incumbent Republican who believes the election was secure in his state. Washington state’s open primary also has a candidate who backs Trump’s unsupported claims, although that’s not the toughest challenge the Democratic incumbent faces.

So far this year, Republican primary voters have split on whether to put election skeptics on the November ballot.

In June, Nevada voters selected former state lawmaker Jim Marchant, who has been repeating the false claims that the 2020 election was stolen from Trump, to face the Democrat in an open race for secretary of state. But in Colorado, GOP voters rejected a local election clerk who has been appearing with Trump allies promoting conspiracies about voting machines and instead chose a Republican who vowed to keep politics out of elections.

And Georgia Secretary of State Brad Raffensperger, who rejected Trump’s plea to “find” enough votes for him to win the state, easily survived a primary challenge to advance in that state’s May primary.

Arizona’s secretary of state race is the most eye-catching and consequential of Tuesday’s primary battles, in part because of Republican state Rep. Mark Finchem.

The retired Michigan police officer and current Arizona House member was at the Capitol on Jan. 6 and contends Trump lost Arizona because of rampant fraud. He backed a controversial and much-criticized state Senate “audit” of the 2020 election results in the state’s most populous county and this year tried to get the Republican-controlled Legislature to notify Congress that Arizona wanted to decertify Joe Biden’s election win.

Finchem also is suing in federal court with a leading GOP contender for Arizona governor to block the use of vote-counting machines in Arizona. The lawsuit contends they are potentially prone to hacking that can change votes. A judge is considering whether to throw out the case.

Finchem’s claims come despite the lack of evidence of any widespread fraud that would have changed the result in Arizona, where Biden beat Trump by just over 10,000 votes.

He maintains that “fictitious ballots” marred the results.

His primary competitors include another state House member, Shawnna Bolick, a Trump supporter who contends the 2020 election was deeply flawed. She said in a televised debate that she would not have certified the election had she been secretary of state, despite it being a requirement to do so absent a court order.

“And I would have been breaking the law at that point and that would have been fine,” she said on the debate carried on Arizona PBS.

The other two Republican candidates are state Sen. Michelle Ugenti-Rita, who acknowledges Biden’s victory and has made election reform a key focus during her 12 years in the Legislature, and Beau Lane, a businessman and political newcomer who has earned the endorsement of Republican Gov. Doug Ducey.

Ugenti-Rita said none of the other candidates has her understanding of election law and that she believes she has broad support across the state.

Lane has said other than a few hiccups and isolated cases of voter fraud, the 2020 election was well run, although he joined the other Republicans in criticizing Democratic Secretary of State Katie Hobbs, who is seeking her party’s nomination for governor.

“Was there organized, rigged fraud that changed the outcome of the election?” he asked. “I have seen no evidence of that.”

Two Democrats are seeking their party’s nomination — former Maricopa County Recorder Adrian Fontes, who lost his seat in the 2020 election, and Arizona House Minority Leader Reginald Bolding. Both criticize Finchem and other Republicans who question the 2020 election results and say a Finchem victory would be dangerous for democracy.