In a large bowl, combine the chicken pieces, diced ham, and diced Swiss cheese. Mix well and set aside.
In a shallow dish, place the flour. In another shallow dish, add the beaten eggs. In a third shallow dish, combine the breadcrumbs, garlic powder, onion powder, paprika, salt, and pepper.
Take a piece of the chicken mixture, form it into a small ball, and roll it in the flour, shaking off any excess. Dip it into the beaten eggs, then coat it with the breadcrumb mixture. Repeat with the remaining chicken mixture.
In a large skillet, heat about 1 inch of cooking oil over medium heat. Once the oil is hot, carefully add the chicken bites in batches, making sure not to overcrowd the pan. Fry for about 3-4 minutes on each side or until golden brown and cooked through.
Remove the bites from the skillet and place them on a paper towel-lined plate to drain excess oil.
Serve warm with your favorite dipping sauce.