Cut the chicken lengthwise into 3/4-inch-wide strips. Put the flour in a shallow dish. Whisk the milk, cayenne, eggs and a pinch of salt and pepper in another shallow dish until combined. Put the breadcrumbs in a third shallow dish.
Dredge the chicken fingers in the flour, shaking off the excess, then dip into the egg mixture, and finally coat with the panko breadcrumbs, pressing to help adhere well. Set aside on a piece of wax paper or a baking sheet.
Heat about 1/2 inch of oil in a large skillet over medium-high heat. Working in batches, fry the chicken fingers, turning occasionally, until golden brown and cooked through, about 3 minutes. Transfer the chicken fingers to a paper towel-lined plate to drain and season with salt. Serve with honey mustard, spicy ketchup and/or ranch dressing for dipping.