Meanwhile Democrats will choose their candidate to run against Republican Rep. Marjorie Taylor Greene in the November general election, while the two parties will also pick nominees in eight state legislative runoffs where no one won a majority in the May 21 primaries.
Turnout is likely to be low, and some congressional nominees could be chosen by a tiny fraction of voters, especially in the the 2nd and 14th districts.
Here's a look at the races:
Republican Chuck Hand grabbed headlines when he walked out of a televised debate. Hand is vying with Wayne Johnson to challenge 16-term Democratic incumbent Rep. Sanford Bishop in the 2nd Congressional District, which sprawls across southwest Georgia, stretching into Columbus and Macon.
Johnson won nearly 45% of the vote in the four-way May 21 primary, to almost 32% for Hand
Hand is one of at least four people convicted of Jan. 6 insurrection crimes who have run for Congress this year as Republicans. He was sentenced to 20 days in federal prison and six months of probation after pleading guilty to a misdemeanor offense.
Both Hand and Johnson agree on the essential challenge — the Republican nominee must find new GOP voters after Bishop won 55% in 2022.
A construction superintendent who lives in rural Butler, Hand has said he is leading a working-class movement to improve economic conditions in one of Georgia's poorest parts. He aims to rally Black and white workers under Trump's banner. But Hand declined to discuss many issues facing Congress.
"I have no urge to play the 'This is what I would do' game. We're not there yet," Hand told reporters after leaving the debate. "In order to do anything, we must first defeat Sanford Bishop."
Johnson has said Hand is unqualified. A U.S. Education Department official under Trump, he says he is better suited to attract some of the Democrats who have long supported Bishop, who are largely Black.
"Hand is weak and shallow on issues of substance that are important to voters, but he is a master of bluster and bravado," Johnson said.
Michael Nixon, who came in third in May with 19%, endorsed Johnson while criticizing earlier criminal charges against Hand that were dismissed, as well as an earlier conviction of Hand's wife for illegal sale of oxycodone.
Republican Brian Jack has argued that the voters of the 3rd District should elect "somebody President Trump trusts to be an America First ally."
His opponent, former state Senate Majority Leader Mike Dugan, has contended that Jack's status as a Washington insider is a liability, saying voters instead prefer his "Georgia values."
The winner will be the favorite to succeed Republican Rep Drew Ferguson, who is stepping down after four terms.
Jack, 36, is a Peachtree City native who worked on Trump's 2016 campaign and served four years as White House political director. He later worked for then-House Speaker Kevin McCarthy.
That experience won him Trump's endorsement and a fundraising haul from top Republicans.
Dugan, a 60-year-old contractor and retired Army officer, touts his experience as a decision maker and coalition builder. He has attacked Jack as a "D.C. insider."
The 3rd District includes some of Atlanta's southern and western suburbs, running south to Columbus, with Republicans typically winning about two-thirds of the vote.
Democrat Maura Keller awaits the GOP nominee in November.
Jack won nearly 47% of the vote in May and was the top vote-getter in 14 of 15 counties. Dugan got almost 25%, carrying his home county of Carroll.
The third- and fourth-place finishers both endorsed Jack.
The Democrats vying to challenge Greene in the 14th District are Clarence Blalock, a 2021 Atlanta City Council candidate, and Shawn Harris, a retired Army general and rancher. Blalock barely led Harris in the four-way primary. The winner faces an uphill fight in a strongly Republican district.
Nominees in eight state legislative seats are being settled in runoffs. Republican incumbent Steven Sainz is trying to hold on to his House District 180 seat in Camden and Glynn counties against challenger Glenn Cook.