Candidates endorsed by former President Donald J. Trump have had mixed success so far in contested Republican primaries for the 2022 midterm elections.

Most of Mr. Trump’s endorsed candidates are running unopposed or face little-known, poorly funded opponents. But many Republican candidates this year, whether endorsed by Mr. Trump or not, have embraced his style of politics, including false claims about the integrity of the 2020 elections.

Here is a look at Mr. Trump’s endorsements in closely watched races today in Georgia, Arkansas and Texas.

Georgia

David Perdue, the Trump-backed former senator, has trailed in public opinion polls and fund-raising in his effort to unseat Gov. Brian Kemp, a Republican who angered the former president by refusing to help overturn the results of Mr. Trump’s 2020 loss in the state. Mr. Perdue has made lies about the 2020 election results a focal point of his campaign. Mr. Kemp has stood by the results, while supporting new restrictions on voting.

Mr. Trump is also supporting Representative Jody Hice in his bid to unseat Secretary of State Brad Raffensperger, a Republican who also refused Mr. Trump’s effort to overturn the state’s 2020 election results. Mr. Hice, a founding member of the House Freedom Caucus, has made Mr. Trump’s baseless claims about the 2020 elections the center of his own campaign.

Herschel Walker, the former professional football player whom Mr. Trump endorsed, has led a crowded field in the Republican primary for Senate, looking to challenge Senator Raphael Warnock, a well-funded Democrat, for the seat Mr. Warnock won in a high-profile special election in early 2021. Mr. Walker has been accused of domestic abuse and embraced skepticism about the 2020 election, but his celebrity and the Trump’s backing have buoyed him in public polling and fund-raising.

In the crowded race for an open congressional seat just north of Atlanta, Mr. Trump endorsed Jake Evans, the son of Randy Evans, Mr. Trump’s former ambassador to Luxembourg. Mr. Evans has been attacked by his rivals for past remarks criticizing Mr. Trump. He has raised less money than Rich McCormick, a former Marine and a physician who narrowly lost a House race in 2020. Dr. McCormick has echoed Mr. Trump’s false claims about the 2020 elections and has refused to concede his own 2020 loss.

Arkansas

Mr. Trump endorsed two candidates who are heavily favored to win their primaries today. Sarah Sanders, Mr. Trump’s former press secretary and daughter of former Gov. Mike Huckabee, is facing Doc Washburn, a conservative talk radio host who was fired after not complying with the radio station’s vaccine mandate.

In the race for attorney general, Lt. Gov. Tim Griffin, whom Mr. Trump endorsed, has raised and spent far more money than his rival, Leon Jones Jr., the state’s former labor secretary.

Texas

Attorney General Ken Paxton has some problems. He has been indicted on criminal securities-fraud charges that are still pending. Several of his top aides claimed he abused his office by helping a wealthy donor. And he has faced abuse-of-power and bribery accusations. But he also has Mr. Trump’s endorsement and that could prove powerful enough to survive a re-election challenge from George P. Bush, the Texas land commissioner and nephew of former President George W. Bush who has clashed with Mr. Trump.