Combine the cream cheese, ham, Swiss, mozzarella, pickles, mustard, cayenne and paprika in a medium bowl.
Stuff the jalapeno halves with the filling and place on a baking sheet lined with parchment.
Set up 3 bowls. In the first, mix together the flour with a pinch of salt and a few cracks of pepper. In the second, beat the eggs with the milk, a pinch of salt and a few cracks of pepper. In the third, place the cracker crumbs.
Coat the stuffed peppers first in the flour mixture, then in the egg mixture and then in the cracker crumbs.
Heat 2 inches of oil in a heavy-bottomed pot until a deep-frying thermometer registers 365 degrees F.
Fry the stuffed jalapenos in batches until golden brown on all sides, about 2 minutes per batch. Alternatively, you can bake the poppers in the oven at 350 degrees F for 30 minutes.