I just want to be certain that what you're asking for are examples of 'fake news' put out there by the conservative media such as Fox News, Alex Jones, Brietbart, etc. I don't want to use up too much of this sites broadband with one single comment so I'll just give you an abbreviated list of fake stories, phony conspiracy theories and outright lies. MIT has actually done a study on how hard-right conservatives have shared more fake news stories than any other group. The University of Oxford project also found that Trump supporters consume largest volume of ‘junk news’ on Facebook and Twitter
Let's begin;
Trump's birther issue claiming Obama was an illegitimate president because he was born in Kenya and is Muslim.
Trump's claim that immediately after 9/11 there were thousands of Muslims standing in New Jersey watching and cheering.
When she was a Fox contributor, Sarah Palin claimed that Democratic government committees --'death panels' -- would decide whether or not you deserved to receive the health care you needed to live.
In May 2017, Fox News reported that Rich’s murder may have been ordered by powerful Democratic Party insiders. “This blows the whole Russia collusion narrative completely out of the water," Fox News personality Sean Hannity said. A week later, Fox quietly retracted its story, but Hannity kept pushing it.
Hannity, described by Pulitzer Prize-winning conservative columnist Bret Stephens as Fox News’s “dumbest anchor,” has harped on the idea that members of the so-called Deep State -- entrenched liberal bureaucrats in the federal government, especially in the U.S. intelligence services -- are undertaking a “soft coup” against President Donald Trump. Former Republican Speaker of the House John Boehner said Hannity, went over to the “dark side” and is not coming back.
Charlottesville. Sean Hannity, questioned the whole event, passing along a conspiracy theory that there weren’t even actual protesters at the rally -- they were “actors hired by a publicity firm.”
Uranium One: Trump recently the Uranium One deal a “modern-day Watergate.” Sean Hannity offered a Fox News headline: “Hillary Clinton's ties to Russian uranium deal largely ignored by anti-Trump media, and other media disasters.” The conspiracy theory was entirely and irrefutably debunked. What Uranium One was a deal that nine members of The Committee on Foreign Investment in the United States approved unanimously. None of them was Hillary Clinton. There was a donor who separately gave Hillary Clinton donations at a time when she was
not Secretary of State. The two things cross in the night -- they have no relation to each other. The members of CFIUS have been very clear Hillary Clinton had nothing to do with approving that deal.
Sebastian Gorka and 'lone wolf'. Former Trump White House aide and regular Fox News talker Sebastian Gorka has blamed liberals and “fake news” for making terrorist attacks more likely in the U.S.“[W]e have to jettison this idea of a ‘lone wolf,’ Gorka said on Fox News. "‘Lone wolf’ was invented as a phrase, was made popular by the Obama administration, to make Americans disconnect the dots." The Obama administration
did not invent, or make popular, “lone wolf” as a phrase.
The right depicted the outspoken student survivors of the mass shooting at Marjory Stoneman Douglas High School as mouthpieces of the FBI, pawns of left-wing activist billionaire George Soros, stooges of the Democratic Party — or all of the above. Fox conspiracy theories claimed that David Hogg was a 'crisis actor' that took advantage of tragedy for political gain.
Then of course one of the most disgusting conspiracy theories ever was that of ultra right-wing conspiracy theorist Alex Jones who claimed that the Sandy Hook murders of 20 kids under the age of 7 and six adults was a hoax, made up as a political tool against gun rights activists. This was the one of the most despicable things any human could do except be the shooter himself because it cause so much pain to the already grieving parents that some received death threats and had to move out of their homes and out of the state several times to escape harassment from right-wingnuts who believed the story.
I'm out of time and room, that will have to do for now, but there's plenty more.