Back court violation
 

I am 90% sure I am correct on this call, but I can't find the rule reference to completely support it.

A1 is dribbling (or holding) the ball in the front court. B1 hits the ball against the leg of A1 and the ball goes back court. A1 is then the first one to touch the ball in back court. Backcourt???

This happened in a game and I told the coach.... Last possession, last touch in the front court, first to touch in the back court is a violation. Am I correct and what is the reference.

Correct. NFHS rule is 9-9-1.
Be aware that the NBA rule is different and since that's what most people see on TV they don't properly understand the HS rule.