The NY Knicks have determined an idiot fan SPIT on Atlanta Hawks superstar Trae Young during Wednesday night's game at MSG ... and now the mouthy fan has been banned indefinitely.

It all went down with around 8 minutes left in the 4th quarter of the Knicks vs. Hawks playoff game ... when Young was trying to inbound.

Video footage shows someone sitting behind 50 Cent appear to spit at Young -- leading Young to comment after the game, "Damn ... crazy!"

Young also asked 50 Cent if he was "good" following the incident.

The NY Knicks were disturbed by the footage and launched an investigation to see if the fan had spit at Young intentionally -- and now, they have detrained it was, in fact, on purpose.

"We investigated the matter and determined that this patron, who is not a season ticket holder, did indeed spit on Trae Young," the team announced Thursday.

"And for that reason, [the fan] is now banned from The Garden indefinitely."

"We apologize to Trae and the entire Atlanta Hawks organization for this fan's behavior. This was completely unacceptable and will not be tolerated in our venue."

The team notes cops are now involved saying -- "We have turned the information over to the appropriate authorities."

In theory, the fan could be prosecuted if officials decide to pursue a case against him.

So far, the fan has not been publicly identified.

Story developing ...