Mix the chicken, green onions, Cheddar cheese, pepperjack cheese, hot sauce, and ranch dressing mix together in a bowl; form the mixture into 1-inch balls with a scoop. Place the balls on a large, flat dish; chill in refrigerator 2 to 3 hours.
Heat oil in a deep-fryer or large saucepan to 375 degrees F (190 degrees C).
Gently press the balls into the flour to coat and shake off any excess. Dip into the beaten egg and then press into bread crumbs. Place the breaded chicken balls onto a plate while breading the rest; do not stack.
Fry the breaded balls in the hot oil until slightly browned, about 1 minute.