While Fox News is home to Trump cheerleaders like Sean Hannity, it also runs a decision desk and a daytime news operation that have declared Mr. Biden the president-elect. That is something many Trump fans do not want to hear, and Newsmax, which frequently reminds viewers it has not projected a winner, is rushing to provide an alternative.

“This whole idea of a president-elect, it is a media fabrication,” Greg Kelly, the 7 p.m. Newsmax host, told viewers last week. “This is not done. This thing could turn.” On Thursday, Mr. Kelly recorded his best numbers yet, pulling 1.1 million viewers for his hour.

Mr. Kelly, a former Fox News correspondent and a son of the former New York City police commissioner, Raymond W. Kelly, said in an interview that his belief in Mr. Trump’s chances is genuine. “I really believe he’s going to prevail,” he said. “It’s a sense I have. Can I articulate perfectly why I thought he was going to win? No. But I’ll say the media has been wrong about him so many times.”