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Two of the most powerful Republicans in Texas are aiming to settle some political scores in Tuesday's GOP primary runoff elections.

And a Republican congressman whose district was the scene of the horrific Uvalde school shooting in 2022 and who's bucked his party on key issues is fighting for his political life against an opponent backed by far-right members of the House.

The showdown grabbing the most headlines is east of Houston, where Texas House Speaker Dade Phelan is facing off against challenger David Covey, who is supported by Texas Attorney General Ken Paxton and former President Trump.

Phelan oversaw the effort last year to impeach Paxton over corruption charges. Paxton was acquitted by the state Senate after the House overwhelmingly impeached the controversial attorney general.

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Texas Attorney General Ken Paxton, left, and Gov. Greg Abbott

Texas Attorney General Ken Paxton, left, and Gov. Greg Abbott (AP Photo/Eric Gay/File)

In response, Paxton has targeted more than 30 GOP incumbent state representatives, with Phelan at the top of the list. And Paxton's most powerful ally, Trump, endorsed Covey.

Three-term Republican Gov. Greg Abbott is looking for payback over the downing in the state House last year of his education plan that would have opened the spigot for taxpayer funding of private schools. The school voucher measure, which was Abbott's top legislative item last year, passed the state Senate, but its defeat in the state House was a rare political setback for Abbott.

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Speaker of the House Dade Phelan in 2021

Speaker of the House Dade Phelan presides, Aug. 26, 2021, in Austin, Texas. (AP Photo/Eric Gay)

Nine GOP state House lawmakers went down to defeat in the state's March primary, with eight more forced into runoffs. All were targeted by either Abbott or Paxton, or by both the governor and the attorney general.

"It’s a power play and definitely a battle for the heart and soul of the Republican Party of Texas, and Gov. Abbott wants to get legislators in there who will support his agenda," veteran Texas-based Republican strategist Brendan Steinhauser told Fox News.

"For Ken Paxton and [Lt. Gov.] Dan Patrick and Donald Trump by proxy, for them, it is definitely trying to take out the person who led the impeachment against Ken Paxton and who stood in the way of Dan Patrick’s agenda in the Senate. All those factors together make a really powerful force for the speaker to overcome."

Donald Trump is endorsing the challenger to Texas state House Speaker Phelan in Tuesday's GOP primary runoff elections

Former President Trump speaks during the National Rifle Association Convention on May 18, 2024, in Dallas. (AP Photo/LM Otero)

Another legislative runoff that may capture some headlines is in suburban Dallas where former Trump campaign adviser and spokesperson Katrina Pierson – with the backing of both Abbot and Paxton – is aiming to unseat state Rep. Justin Holland.

A Republican congressional primary runoff sure to grab national attention is in the southwestern part of the state, where GOP Rep. Tony Gonzales is running for a third two-year term representing a majority Hispanic district that stretches along the U.S.-Mexico border  

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With more than 800 miles of U.S.-Mexico border, Texas’s 23rd district has the largest stretch of the border territory of any congressional district. The district is also home to Uvalde, where two years ago 19 children and two adults were murdered in an elementary school shooting.

Gonzales, who has bucked his party on gun safety, immigration and same-sex marriage, is facing off in the runoff against gun rights advocate Brandon Herrera, who's known for his gun-themed YouTube channel titled "The AK Guy."

Rep. Tony Gonzales

Rep. Tony Gonzales, R-Texas (Bill Clark/CQ-Roll Call via Getty Images/File)

While Gonzales is backed by Abbot and Lt. Gov. Dan Patrick, Herrera is backed by controversial Rep. Matt Gaetz of Florida and other far-right House members.

Steinhauser noted that Herrer is branding the showdown as "an establishment-versus-far-right populist race" and that Gonzales "knows that he needs to [protect] his right flank"

But he added that "Tony has a pretty big presence in the conservative eco ecosystem. He’s on Fox News a lot, talking about the border."

Get the latest updates from the 2024 campaign trail, exclusive interviews and more at our Fox News Digital election hub.