Bring a large pot of lightly salted water to a boil. Add macaroni and cook 7 minutes or per package directions; drain.
Meanwhile, melt butter in a saucepan over medium heat. Whisk in flour, cooking until bubbly. While whisking, add 1 1/4 cups of the milk in a thin stream. Season with salt, black pepper and cayenne. Bring to a simmer and cook 2 minutes. Remove from heat and mix in 1 cup of the cheddar and the American cheese. Fold into macaroni in a large bowl. Let cool slightly, then stir in mozzarella and remaining 1 cup cheddar. Spread mac and cheese onto a rimmed sheet. Cover with plastic and refrigerate overnight.
Use a scoop to spoon out about 1/4 cup of the mixture at a time and shape into 2- to 3-inch balls, compressing slightly.
Whisk eggs with remaining 1/4 cup milk. Dip balls in egg mixture, then coat in panko.
Heat oil in a deep 4-quart pot to 360° on a deep-fry thermometer. Fry 6 or 7 mac and cheese bites at a time for 3 to 4 minutes per batch, until golden. Serve immediately.
