In a large bowl, mix together cream cheese, Monterey Jack cheese, cheddar cheese, diced jalapeños, and ranch dressing mix until well combined.
Form the mixture into 1-inch balls and place on a parchment-lined baking sheet. Freeze for 15 minutes to firm up.
Set up a breading station with three shallow bowls: one with flour, one with beaten eggs, and one with panko breadcrumbs.
Roll each cheese ball in flour, then dip in egg, and finally coat thoroughly with panko breadcrumbs.
Heat vegetable oil in a deep pot to 350°F. Fry the bites in batches for 2-3 minutes until golden brown.
Remove with a slotted spoon and drain on paper towels. Serve hot with ranch dressing for dipping.