TMZ Sports is told ... the incident went down during a fall league contest between Arlington and Oak Hills at Santiago High School in Corona, California on Saturday, Oct. 21.

At some point in the second half, witnesses claim Oak Hills head coach Rob Alexander got upset with referee Brandon Knapper over his officiating ... and an argument ensued.

In a clip we obtained of the game, 26-year-old Knapper -- a former college basketball player at West Virginia, Eastern Kentucky and Cal State San Bernardino -- can be seen approaching Alexander near Oak Hills' bench and briefly talking to him ... before unleashing his fist on the coach's face.

Knapper appeared to land more punches on Alexander as he fell to the court ... before players and others in attendance got involved.

We're told cops responded to the scene ... and Alexander was taken to the hospital. The game did not continue.

Law enforcement tells us Alexander requested prosecution against Knapper, who turned himself in and was charged with battery causing serious bodily injury and assault by means likely to produce great bodily injury -- both felonies.

Knapper was booked in the Riverside County Sheriff's Department jail on Sunday ... and his bail was set at $25,000. He was released on Wednesday.

Oak Hills' Hesperia Unified School District released a statement to TMZ Sports ... condemning Knapper's "senseless and shameful" actions.

"The District is thankful for the swift and decisive action taken by the event promoters and local law enforcement. We are also happy to report that Coach Alexander is in good spirits and looking forward to returning to coaching and teaching as soon as possible."

"We have the utmost confidence that law enforcement, CIF, and Oak Hills High School, with the support of the District, will investigate the incident thoroughly and handle it appropriately."