Ohio Republican Rep. Jim Jordan wants to be speaker of the House, but his run at the throne, while considered a long shot, could put him in a position to land something else he prizes: the power to shape GOP policy toward one of the investigations surrounding President Trump and his alleged ties to Russia.

The Republican chairmen of the House Judiciary and Oversight and Government Reform committees are retiring in January, opening the party’s top spots on two panels uniquely equipped to harangue the executive branch — authority they leveraged this year to doggedly scrutinize FBI and Justice Department officials investigating allegations Trump’s campaign conspired with Moscow to influence the 2016 presidential election. As a member of both panels, Jordan has been an influential force in that probe. But he and other Trump allies in Congress are frustrated at party leaders’ reluctance to bring the full weight of congressional censure upon those in law enforcement who they assert are biased against the president.

How aggressively House lawmakers continue to examine this aspect of the Trump-Russia saga depends on the outcome of Tuesday’s elections, what further charges may emerge from special counsel Robert S. Mueller III’s investigation, and anticipated staffing changes at the Justice Department. But all of the 10 Republican and Democratic congressional officials The Washington Post spoke to for this report — most of whom requested anonymity to offer their candid assessments about pending political power struggles — said they believed the Judiciary and Oversight committees would continue to devote attention to Russia-related matters next year regardless of which party holds the House majority.

That means the GOP’s eventual choice of committee leaders will reveal whether House Republicans intend to keep hammering those who challenge the president and how much sway Trump’s allies will wield over congressional oversight of the administration during the second half of his first term.

Jordan is not the only Trump loyalist up for a key committee leadership post. Rep. Mark Meadows (R-N.C.), another close ally of Trump’s, could make a bid to lead Republicans on the Oversight and Government Reform committee, GOP aides say, leaving Jordan to compete for Judiciary. Meadows has denied he is interested in that job, saying recently that: “I’m not in it for me; I’m in it for other people.”

“Congressman Jordan certainly would be a very credible chairman of OGR . . . He would be a great chairman for both [panels],” Meadows said in a separate interview. It’s a shame, he added, that Jordan can’t hold two leadership posts.

Jordan, who did not respond to interview requests, has not announced plans to compete for anything but the speaker’s gavel. And before they retire, the current chairmen, Reps. Bob Goodlatte (R-Va.) and Trey Gowdy (R-S.C.), are expected to deliver a report summarizing the joint probe’s findings thus far. Still, some party leaders have expressed apprehension about giving a firebrand Trump defender the unilateral subpoena power that comes with a committee chairmanship, if Republicans keep the House majority.

Partisan division has already all but splintered the House Intelligence Committee during its investigation of Russian interference in American politics. And although the GOP has been critical of what it says are bias and unprofessionalism in federal law enforcement’s probes of Hillary Clinton and the Trump campaign, top Republicans often have eschewed the more incendiary tactics employed by Jordan and Meadows, who have gone so far as to call for the impeachment of Deputy Attorney General Rod J. Rosenstein, who oversees Mueller’s work.

Yet Jordan is well liked by his peers, and senior Republican figures know his bid to lead the GOP could build momentum and spoil the plans of Majority Leader Kevin McCarthy (R-Calif.), who hopes to take over from Speaker Paul D. Ryan (R-Wis.) when he retires in January. To ensure a smooth transition from Ryan to McCarthy, some GOP officials anticipate that the leadership may need to cut a deal with Jordan.

A spokesman for McCarthy did not respond to interview requests.

Committee leadership positions have always been choice bartering tools to quell challengers. Those decisions won’t be settled until the GOP’s steering committee convenes in January and will be heavily influenced by the election’s outcome.

According to recent polling, Democrats are expected to win the House majority on Tuesday — but that is far from guaranteed. And if Democrats do end up in control, their oversight agenda is all but established.

The ranking Democrats on the Judiciary, Oversight and Intelligence committees — Reps. Jerrold Nadler (N.Y.), Elijah E. Cummings (Md.) and Adam B. Schiff (Calif.), respectively — have said that as chairmen of those panels, they intend to examine whether Trump’s surrogates coordinated with Russian authorities in 2016 and delve into the Trump family’s finances and what they see as the grant of questionable security clearances to those close to the president.

In that environment, some GOP officials say, it would be advantageous to have an attack dog like Jordan leading the Republican side — as a “defender” for Trump, as one GOP aide put it. Many in the party fear that Democrats, should they retake the majority, will try to impeach the president.

Others argue it would behoove the Republican Party to strike a middle ground by appointing committee leaders who are unquestionably conservative but ultimately less combative.

“I’ve developed a reputation of making things about policy and not about people or personalities,” Rep. Steve Russell (Okla.), who is hoping to become the top Republican of Oversight and Government Reform, said when asked how he would compare himself with a challenger such as Jordan or Meadows.

Russell is the only Republican panel member formally seeking to replace the departing chairman, Gowdy. He said his top agenda items for next year do not necessarily include continuing to pursue the Justice Department’s handling of the Trump and Clinton probes.

“If there are investigations that need to occur, then let’s do them,” Russell told The Post, but he noted that his preference would be to focus on overhauls in areas of the federal government, such as the Postal Service and security for Foreign Service personnel, where “there is a lot of common ground.”

On the Judiciary Committee, Republican Reps. Douglas A. Collins (Ga.) and Steve Chabot (Ohio) have made similar cases — that they are the responsible, less-polarizing choice to head that panel. Publicly, neither has been as fixated on Trump and Russia as Jordan and Meadows have.

But Collins has produced evidence that a former top FBI official involved with the Trump and Clinton probes retained his high-level security clearance for months after being removed from those investigations for exhibiting bias. Collins also revealed at a contentious public hearing with Rosenstein in June that the former FBI official, Peter Strzok, had an “out of scope” polygraph while working on those probes.

Jordan made headlines at the hearing for lambasting the deputy attorney general. Collins, during a break, shook Rosenstein’s hand.