The heavyweight boxing legend came face to face with the Youtuber-turned-fighter at Fanatics Fest at the Jacob K. Javits Convention Center in New York City Sunday ... and, when they come together in the center, Tyson gives Paul a quick left to the chest.

Tyson and Paul exchange words before they start moving back toward each other ... where Tyson full-on shoves JP -- cracking up at his 27-year-old opponent.

Corralled into standing face to face once again, the two finally let photographers get the photos they need ... before Paul gets MT back with his own push.

Mike seemed giddy during their whole exchange ... seemingly not a lot of malice here -- but, Paul appeared none too happy about the champ clowning him in front of all those cameras.

Not the first time the two have done a press conference like this, remember. The fight was initially supposed to happen last month, but the two fighters agreed to push it back after Mike suffered a medical emergency on a plane in late May.

Tyson still trash talked his opponent after his medical scare -- saying his emergency only bought Paul more time. Jake's promised him no mercy in the ring -- so, don't expect anyone to take it easy come November 15.