Vince Fong, a state lawmaker in California and onetime aide to former Speaker Kevin McCarthy, won a special election on Tuesday to fill his seat — representing the most conservative district in the deep-blue state. Mr. Fong succeeds Mr. McCarthy nearly five months after he resigned from Congress, following his ouster from the speakership.

Mr. Fong will now serve until the term expires in January and will again face his Republican opponent — Mike Boudreaux, the longtime sheriff of Tulare County — in the fall to seek a full term.

Georgia, Idaho, Kentucky and Oregon also held primary contests on Tuesday, with presidential primaries in Kentucky and Oregon yielding notable protest votes against President Biden and former President Donald J. Trump.

Here are some takeaways.

Biden met significant resistance in the Kentucky primary, and a protest vote against him in Oregon faltered.

Nearly 30 percent of voters in the Democratic primary in Kentucky backed an option that wasn’t Mr. Biden, a notable underperformance for the president among Democrats in the state. The protest vote against Mr. Biden there was nearly double that against Mr. Trump, who won about 85 percent of the vote in the Republican primary. Turnout also plunged in the Democratic primary, with about 184,000 votes tallied, compared with the more than 537,000 recorded in 2020.

In Oregon, a write-in campaign in protest of Mr. Biden’s handling of the war in Gaza underperformed significantly, with less than 5 percent of all votes in the Democratic primary going to write-ins. In neighboring Washington State, the uncommitted ballot option got nearly 10 percent of the vote in the Democratic primary in late March. Mr. Trump was unopposed in Oregon’s Republican primary.