Four years ago, the Green Party candidate played a significant role in several crucial battleground states, drawing a vote total in three of them Wisconsin, Michigan and Pennsylvania that exceeded the margin between Donald J. Trump and Hillary Clinton.
This year, the Republican Party has been trying to use the Green Party to its advantage again, if not always successfully.
In Wisconsin, a G.O.P. elections commissioner and lawyers with ties to Republicans tried to aid attempts by Howie Hawkins, the Green Partys presidential candidate, to get on the ballot there, which were ultimately unsuccessful. In Montana, state regulators found that the Republican Party had violated campaign finance laws as part of an effort to help the Greens in five down-ballot races, including for senator and governor.
And in Western Pennsylvania, petitioners from Florida and California were brought in to gather signatures for Mr. Hawkins by an outside firm whose actions Mr. Hawkins and the party said they could not account for. Mr. Hawkins also did not make the ballot there.
With Mr. Trump trailing Joseph R. Biden Jr. in most national and swing-state polls, Republicans are again trying to help third parties that may appeal to Democratic voters and siphon off votes from Mr. Biden. This is taking place alongside a broader pattern of disinformation and skepticism by the president and his allies that has sown confusion and undermined confidence in the election.
Supporters of the president have also been trying to advance the candidacy of Kanye West, the billionaire hip-hop artist, confident that he can cut into Mr. Bidens vote total. Democrats have portrayed the effort as a dirty trick and exploitative of Mr. West, who has bipolar disorder.