UEFA has fined Everton 30,000 euros after a fan tried to punch an opposing team's goalkeeper when a clash between players spilled toward the stands.
UEFA says Everton was guilty of "aggressions by supporters against players" during a Europa League game against Lyon last month.
The fan was holding a child with one arm when he targeted Lyon goalkeeper Anthony Lopes during the melee.
Everton said it would ban the supporter from attending games.
The ugly scenes were sparked by an Ashley Williams foul on Lopes, who was then pushed in the melee towards the advertising hoardings at the Gladys Street end, where an irate fan carrying a young child slapped him on the head twice.