Since his rise to the presidency, Donald J. Trump has claimed enormous wealth as proof that he is an anti-establishment ally of the working class, not beholden to corporate donors or special interests.

The Republican Party, eyeing control of the Senate next year, is trying to mimic his success with a cohort of candidates who in the past might have been attacked as a bunch of rich men but this year will be sold as successful outsiders in the Trump mold.

The decision by Ohio voters on Tuesday to nominate Bernie Moreno to take on Senator Sherrod Brown, a Democrat, is the capstone of a year that has crowned nominees — or anointed clear front-runners — with remarkable wealth in Pennsylvania, Wisconsin, West Virginia, Montana and now Ohio.

That might match the party’s presumptive nominee, Mr. Trump, but with backgrounds in banking and hedge funds, properties in Connecticut and Laguna Beach, Calif., and education credentials from Princeton and the Naval Academy, some in the 2024 class feel more like the days of Mitt Romney, worth around $174 million, and John McCain, a Naval Academy graduate who married into a beer-distributing empire, than the current moment when blue-collar credibility is the currency of the realm.

The intentional decision by Republicans in Washington, D.C., to get behind candidates with enormous personal fortunes will most likely give the party a boost as it struggles for campaign cash against the Democrats’ formidable grass-roots fund-raising operations. But the sheer affluence of the candidates — and how they made their money — is sure to be a factor in the fight for Senate control.