Former President Donald J. Trump’s pull among likely Republican voters is less dominant in Iowa than it is nationwide, though he still leads his nearest rival, Gov. Ron DeSantis of Florida, in the key early state by double digits, according to a new New York Times/Siena College poll.

The survey of 432 likely Iowa caucusgoers was taken before a third indictment against Mr. Trump was made public on Tuesday, this one charging him with federal crimes connected to his efforts to cling to office after losing re-election in 2020.

But any dent in his dominance in the Hawkeye state may have more to do with factors like personality flaws and voters’ fatigue after eight years of Trumpian drama than his latest legal travails. Iowa Republicans showed some real doubts about which candidate — Mr. Trump or Mr. DeSantis — is more moral, likable or able to beat President Biden in 2024.

Overall, Mr. Trump has the support of 44 percent of Iowans polled, 10 percentage points lower than the commanding position he holds with Republicans nationwide. Mr. DeSantis is second with 20 percent, slightly better than his 17 percent standing nationwide. Senator Tim Scott of South Carolina has the support of 9 percent of likely Iowa Republican caucusgoers, triple his national standing. Mr. Scott’s favorability rating among Iowa Republicans — 70 percent — is on par with Mr. Trump’s 72 percent and just behind Mr. DeSantis’s 77 percent.

Further down, the entrepreneur Vivek Ramaswamy, former Gov. Nikki Haley of South Carolina and former Vice President Mike Pence each have single-digit support. Support for former Gov. Chris Christie of New Jersey did not reach a full percent.

The poll suggests that Mr. DeSantis’s efforts in Iowa have been having an effect, but that the challenge of defeating Mr. Trump there is doubly complicated: Several rivals are siphoning off the support he would need from voters who are open to alternatives to the former president, and Mr. Trump’s voters are still overwhelmingly behind him. And as with the national race, it seemed Mr. DeSantis was failing to win over voters with the issues he has made central to his campaign, including defeating so-called woke ideologies.

The state is the first of the G.O.P. presidential nominating contests, and it looms large for Mr. Trump’s comeback. In 2016, Senator Ted Cruz of Texas edged out Mr. Trump and Senator Marco Rubio of Florida. Iowa’s Republican base is strongly religious and white, and its position on the political calendar has ensured that voters get a good look at the candidates before they go to the caucuses. The power of evangelical leaders, some of whom are ready to move past Mr. Trump, could give other candidates an advantage when Iowans caucus on Jan. 15.

A Trump victory in Iowa — despite mounting legal challenges — could give the former president a clear path to the nomination.

Even Iowa Republicans who say they favor other candidates could still swing Mr. Trump’s way.

“Each indictment gets me leaning toward Trump,” said John-Charles Fish, 45, a Waukon, Iowa, social media consultant who said he still supported Mr. DeSantis, but barely. “It wouldn’t take much for me to change my mind,” he said.

For Mr. DeSantis and other competitors, the Iowa survey yielded glimmers of bright spots. About 47 percent of Mr. Trump’s supporters said they would consider other candidates. Among Republicans with at least a college degree, Mr. Trump and Mr. DeSantis are tied at 26 percent when the whole field is under consideration.

In a head-to-head match between the front-runner and his closest rival, Mr. Trump leads Iowa handily, 55 percent to 39 percent, but he is well behind Mr. DeSantis among college-educated Republicans, 38 percent to 53 percent.

According to the poll, Mr. DeSantis is seen as the more moral candidate, and although the Florida governor has been knocked for some awkward moments on the campaign trail, he is seen as considerably more likable than Mr. Trump. More than half of those surveyed said the term “likable” was a better fit for Mr. DeSantis, compared with 38 percent for Mr. Trump.

The poll also suggests that Mr. DeSantis’s argument that he is the more electable Republican may be resonating with voters, at least in Iowa. Just under half of those surveyed said Mr. Trump is the candidate more able to beat Mr. Biden, while 40 percent said Mr. DeSantis is. Nationally, Mr. Trump holds a 30-percentage-point lead on the same question.

Robert Corry, a business consultant in Grinnell, Iowa, praised Mr. DeSantis’s stewardship of Florida’s sprawling economy, his ability to “get things done” and his “exemplary, outstanding life.”

The contrast between Mr. DeSantis and Mr. Trump “couldn’t be greater,” said Mr. Corry, 55, who worries that making Trump the Republican nominee could cost the party another election.

Still, Mr. Trump remains a powerful and resilient force among Republicans, nationally and in Iowa. Of the Iowans supporting the former president, 97 percent say they support him strongly, compared with the 76 percent of Mr. DeSantis’s supporters who said the same for him. Among those who support other candidates, just over half — 54 percent — say they back their candidate strongly.

“As far as the other candidates go, I feel that they’re all RINOs,” said Pamela Harrmann, 74, a retired intensive care nurse in Paullina, Iowa, and a Trump supporter who referred to the former president’s opponents as Republicans in name only. “And they’re all with the left agenda. They’re just covered up.”

Tuesday’s indictment, which accuses Mr. Trump of defrauding the nation in his quest to subvert the will of its voters after he lost the 2020 election, may not change the depth or intensity of the front-runner’s support. Nor does the perception of Mr. DeSantis as the more moral candidate seem to carry much weight among the voters who might be expected to be more sensitive to such traits.

Half of white evangelical Republicans in Iowa support Mr. Trump, six percentage points more than the former president’s overall Republican support. In contrast, Mr. Pence, a religious Christian who counted on white evangelical backing, has the same 3 percent support among white evangelicals in Iowa that he has among the larger field of Republican caucusgoers. The 48 percent of white evangelicals who hold a favorable opinion of Mr. Pence are slightly outnumbered by the 49 percent who dislike him.

Those numbers come despite the call from one of Iowa’s most powerful and influential conservative Christian leaders, Bob Vander Plaats of the Family Leader, for his flock to turn the page on the Trump era.

For die-hard Trump backers such as Dave Peterson, a 60-year-old truck hauler and farmer in Audubon, Iowa, the latest criminal charges against Mr. Trump have only solidified their support.

The three indictments handed down to Mr. Trump thus far are “all a bunch of crooked B.S., trying to keep him from running,” Mr. Peterson said. An expected fourth indictment in Fulton County, Ga., concerning Mr. Trump’s efforts to reverse Mr. Biden’s victory in the state would do nothing to shake his view of a multipronged effort to stop a Trump comeback, he added.

Robert Novak, 76, a retired business owner, agreed that the investigations are unfounded and politically motivated.

“Does he say things he shouldn’t say? Absolutely,” Mr. Novak said. “But here’s the thing, and people need to know this: President Trump is a leader. He is not a politician.”

Unfounded conspiracies surrounding the 2020 election appear to be at the heart of Mr. Trump’s support. Julie Bates, a 63-year-old retiree in Des Moines, said she found it suspicious that the Covid-19 virus was “accidentally released at a very important time in our election period.”

But like many other Iowans, Ms. Bates has seen enough of the other Republican candidates to feel comfortable voting for them, although for now she supports Mr. Trump. Mr. DeSantis “is sticking out for me,” she said. Still, like a strong majority of Iowa Republicans, 67 percent, she said she preferred a candidate who was focused on “restoring law and order in our streets and at the border” than one trained “on defeating radical ‘woke’ ideology in our schools, media and culture.”

Ms. Bates said Mr. DeSantis has taken his crusade against such ideology too far, citing a school district in Urbandale, Iowa, that has begun removing books from its libraries.

“That’s the same as when they used to do book burning,” she said.

Camille Baker contributed reporting.

The New York Times/Siena College poll of 432 likely Iowa Republican caucusgoers was conducted by telephone using live operators from July 28 to Aug. 1, 2023. The margin of sampling error is plus or minus 5.9 percentage points. Cross-tabs and methodology are available here.