Trump -- the Republican presidential nominee -- took to Truth Social late Sunday to make wild, unsubstantiated claims about Biden ... while also mocking his cognitive issues.

In a series of posts ... Trump alleged on the social media platform that Biden never had COVID and that he was a threat to democracy.

As you know, Biden said he tested positive for COVID last week while he was in Las Vegas for the NAACP National Convention. He flew home to Delaware for some R&R as he recovered from the disease.

But, Trump didn't stop there in his criticism of Biden ... he went on to question who was really running the country since he believes Joe "has no idea where he is."

The ex-Prez also ridiculed Biden by saying he would wake up Monday and not remember that he dropped out of the race. Trump noted that if Biden can't run for office, then he can't run the nation ... something that many Republicans have echoed since the drop-out news.

Earlier in the day, after Biden made the announcement to abandon his campaign, Trump slammed the lifelong Democrat for being unfit to be president.

Meanwhile, Joe has thrown his full support behind his VP Kamala Harris to be the next commander-in-chief. Kamala seems to be the odds-on favorite to become the Democratic party's new nominee.