The son of wrestling legend The British Bulldog (real name Davey Boy Smith) is a wanted man -- after throwing a cup of coffee straight in the face of WWE Hall of Famer Jake "The Snake" Roberts.

New Orleans PD is investigating an incident that occurred the day before WrestleMania 34 -- when Davey Boy Smith Jr. and Roberts had an altercation during an autograph-signing sesh on Canal St.

The Snake told cops Davey Boy Jr. -- a former WWE wrestler himself -- threw coffee at him after a dispute, and police tell us he's now "wanted for battery in connection with this incident," as first reported by Pro Wrestling Sheet

Cops say Roberts, 62, reported no major injuries.

But get this -- Smith spoke openly about the incident the same day it happened ... telling WrestleZone he confronted The Snake because he previously dissed his dead father.

The 32-year-old wrestler says he challenged Jake to a fistfight ... and threw the hot cup of Joe after The Snake told him to, "F**k off."

Stay tuned ...