In a large bowl, mix together the cream cheese, chicken, hot sauce, mozzarella, Cheddar, salt, pepper, and garlic until evenly combined. Transfer into a 8 by 8-inch square baking dish, lined with parchment paper. Using a rubber spatula, firmly press down the mixture to create a smooth even layer. Cover with plastic wrap and freeze for 3 hours.

Pour the flour into a shallow baking dish. Whisk the eggs in a separate baking dish. Combine the breadcrumbs and panko in a third baking dish. Set aside.

Invert the chicken and cheese mixture onto a cutting board, and remove the parchment paper. Cut in half, then cut into 20 even thin "sticks." Working as quickly as possible, coat each stick in flour, then dip into the egg, then in to the breadcrumbs, once again into the egg, and once more into the breadcrumbs. Place breaded mozzarella sticks onto a baking sheet lined with parchment paper. Freeze for 1 hour before frying.

Fill a heavy duty dutch oven halfway up with oil, and heat to 360 degrees F, using a deep-fry thermometer. Once hot, add in a few of the sticks at a time, and fry until golden brown and crispy, turning over halfway, about 2 to 3 minutes in total. Strain and place on a wire rack set over a baking sheet. Continue frying the remaining mozzarella sticks. Serve with ranch or blue cheese on the side for dipping.