Combine shredded pepper jack and diced jalapeños in a bowl.
Roll into 1 1/2-inch balls, pressing firmly. Place on a cookie sheet.
Freeze for 30 minutes to help them hold shape.
Heat vegetable oil to 350°F (175°C).
Set up bowls with flour, beaten egg mixed with milk, and seasoned bread crumbs.
Coat each ball in flour, dip in egg mixture, then coat with bread crumbs.
Fry in batches for 3–4 minutes until golden brown.
Drain on paper towels. Serve hot with dipping sauces.