I don't think I've ever seen fake news that was left wing, unless you consider something like the New York Times left wing (it's not, it's centre-right), in which case there is a lot of spurious news in the "left wing" of mainstream media.

That said, they usually at least get the facts right, they just like to lie by omission, pushing an agenda by cherry-picking data. Far right media goes one step further and often just directly publishes false data to mislead its readers.