Voters in Louisiana are headed to the polls on Saturday for the Republican Senate primary, which will pose a fresh test of President Trump’s ability to punish a lawmaker in his party who has crossed him.

The incumbent, Bill Cassidy, is one of seven Republican senators who voted to convict Mr. Trump in his impeachment trial after the Jan. 6, 2021, attack on the U.S. Capitol. Mr. Trump is supporting a challenger, Representative Julia Letlow. John Fleming, the state treasurer, is also vying for the nomination. Many observers expect the race to continue into a June runoff. Here’s what to watch in one of the marquee intraparty contests of 2026:

How will President Trump’s involvement factor into the outcome?

The primary in Louisiana is part of a larger push by Mr. Trump to involve himself in G.O.P. primaries and to try to oust lawmakers who have clashed with him. In Indiana this month, most of the primary challengers he supported defeated state lawmakers who defied him on redistricting. Mr. Trump is also backing a challenger trying to defeat a House member in Kentucky on Tuesday.

In the Louisiana race, the president has been outspoken about his preference.

Mr. Trump has openly disparaged Mr. Cassidy, calling him a “flake” and “a very disloyal person.” On Friday, Mr. Trump praised Ms. Letlow on social media, calling her a “total winner” who “will never let you down.” In January, Mr. Trump endorsed Ms. Letlow before her candidacy was official.

For his part, Mr. Cassidy has pointed to areas where he and Mr. Trump have found common ground, even as he acknowledges the president’s vendetta against him. Ms. Letlow has touted her endorsement from Mr. Trump, while Mr. Fleming has also praised the president, calling himself “the only conservative MAGA Republican” in the race and highlighting his tenure as an aide in the first Trump administration.

Which version of Republican politics and proximity to Mr. Trump will Louisiana voters favor? The answer will offer some clues about the direction of the party.

Many see a runoff coming. Will Mr. Cassidy be shut out?

To win outright on Saturday, a candidate will need to receive more than 50 percent of the vote. If that doesn’t happen, the top two vote-getters will compete in a runoff, to be held on June 27.

Strategists and observers said in the lead-up to Saturday that a runoff appeared likely. Less clear to them was who would be part of it. Polls have shown Mr. Cassidy is not a sure bet to advance.

The three-way contest has been full of attacks.

Ms. Letlow and her allies have repeatedly taken on Mr. Fleming. Ms. Letlow’s campaign has cast Mr. Fleming as a career politician who would put his business interests above his constituents. Mr. Fleming has countered by reminding voters of Ms. Letlow’s past comments in favor of diversity, equity and inclusion initiatives, a line of attack Mr. Cassidy has also taken up.

Ms. Letlow has responded by saying D.E.I. had been “hijacked by the left” and that she had “fought against it ever since.” She has also pointed out both of her rivals’ past criticisms of Mr. Trump.

Mr. Cassidy and his allies have spent big on the race. If he does make a runoff, that could be one reason why.

How will changes to the way the primary is conducted affect turnout and the result?

For the first time since the 1970s, Louisiana will hold a closed-party primary for Senate. For decades, a single primary was open to candidates and voters regardless of party affiliation.

The change could mean a more conservative primary electorate, which some strategists suggested could pose a challenge for Mr. Cassidy. Mr. Cassidy’s campaign has been courting unaffiliated voters, who are eligible to participate in the newly closed primary.

Democrats are holding their own primary on Saturday; the winner will be a significant underdog in the general election, given the state’s conservative tilt.

Another wild card: The state postponed its House primaries after the Supreme Court struck down Louisiana’s congressional map last month, while keeping its Senate primary scheduled for Saturday. The shift sowed some voter confusion.

As early voting began two weeks ago, Mr. Fleming’s campaign sent out texts and emails reminding voters that the Senate primary was still a go. Mr. Cassidy, meanwhile, has been critical of the decision to split the dates of the primaries.

Michael Gold and Emily Cochrane contributed reporting.