After bringing some 60 lawsuits, and even offering financial incentive for information about fraud, Mr. Trump and his allies have failed to prove definitively any case of illegal voting on behalf of their opponent in court — not a single case of an undocumented immigrant casting a ballot, a citizen double voting, nor any credible evidence that legions of the voting dead gave Mr. Biden a victory that wasn’t his.

“It really should put a death knell in this narrative that has been peddled around claims of vote fraud that just have never been substantiated,” said Kristen Clarke, the president of the National Lawyers’ Committee for Civil Rights Under Law, a nonprofit legal group, and a former Justice Department attorney whose work included voting cases. “They put themselves on trial, and they failed.”

Yet there are no signs that those defeats in the courts will change the trajectory of the ongoing efforts to restrict voting that have been core to conservative politics since the disputed 2000 election, which coincided with heightened party concerns that demographic shifts would favor Democrats in the popular vote.

The false notions have lived on in Mr. Trump’s Twitter and Facebook feeds; on the television programming of Fox News, Newsmax and One America News Network; and in statehouse hearings where Republican leaders have contemplated more restrictive voting laws based on the rejected allegations.