Many accounts say that the James J Corbett- Tom Courtney fight, filmed on 08-September-1984 was the first fight film. However, on 14-June-1894, WKL Dickson of the Edison company filmed a fight between lightweight boxers Mike Leonard, the Fashion Plate, the Beau Brummel of the Prize Ring, and Jack Cushing. The original production had six one-minute rounds, each on a Kinetoscope reel. It was filmed in a tiny ring in Edison's Black Maria studio in West Orange, New Jersey.
I couldn't find much about Jack Cushing, but here is an ad for a vaudeville appearance by Mike Leonard from the 25-August-1895 Washington Morning Times.
What survives of the fight looks like a good scrap.