President Trump’s effort to oust Republicans deemed insufficiently loyal faced a key test on Tuesday as Indiana voters decided whether to back state senators who opposed redistricting and whom the president wanted out.

Mr. Trump’s political payback campaign, which will extend later this month to intraparty clashes in Georgia, Kentucky and Louisiana, comes as his poll numbers sag.

Also on Tuesday, Ohio voters were picking candidates for a Senate race that is seen as essential for Democrats hoping to win control of Congress. And in Michigan, Republicans were hoping to flip a crucial State Senate seat in a competitive district.

Taken together, Tuesday’s elections will offer a window into Mr. Trump’s influence as the war in Iran and high gas prices are raising alarms for Republicans and fueling Democratic optimism about the general election in November.

With polls in much of Indiana set to close at 6 p.m. Eastern, here is what to watch for:

Indiana Was an Outlier

Several Republican-led states quickly fell in line last year when Mr. Trump demanded redrawn maps to improve Republicans’ chances in Congress in the midterms. But Indiana was different.

Republicans hold large legislative majorities in Indiana, but a critical mass of state lawmakers opposed the idea. They stuck to their stance even when the president threatened political retribution, and even as some Democratic-led states moved to redraw their own maps to the Democrats’ benefit.