The most recent fake one that I've seen, with its supports absolutely adamant that it's real, is the "Clinton didn't really win the popular vote, Trump did!" thing. They defend it to the day they die, despite the fact that it's flatly contradicted by all official sources, can be traced back to the guy who made it up, and is based around factually incorrect statements about how votes are tabulated.
I saw this on Facebook from Judge Jeanine Pirro. I went and checked, and couldn't find any returns that supported it.
Not that the left is innocent in all of this. I still keep seeing that fake quote about Trump saying that Republican voters are idiots who will believe anything. How many times do you have to point out that it's fake for people to stop circulating it?
Another friend of mine posted the Trump quote and I linked to Snopes showing it was a fake, figuring he would see that as authoritative.. One of his friends said "Yeah, and who runs Snopes?!?" Another one of his friends said something like "So what if it's not true? After all the lies he told about Hillary, we need to keep circulating it a million times!" SMH.