In a mixing bowl, combine the shredded Monterey Jack cheese, cream cheese, and diced jalapeños. Mix until well combined.
In a separate bowl, whisk the eggs until blended.
In another bowl, combine the flour, garlic powder, onion powder, paprika, and salt.
Take a small amount of the cheese and jalapeño mixture and form it into a ball, about the size of a golf ball. Repeat until all the mixture is used.
Roll each cheese ball in the flour mixture, then dip it into the beaten eggs, and finally coat it with breadcrumbs. Set aside.
Heat oil in a frying pan over medium heat. Once hot, carefully add the cheese balls in batches, making sure not to overcrowd the pan.
Fry until golden brown, about 3-4 minutes per side. Use a slotted spoon to remove the bites and place them on paper towels to drain excess oil.
Serve hot with your favorite dipping sauce.