In a large Ziploc bag, mix in lime juice, mustard, 1-½ Tablespoons salt, and 2 teaspoons pepper. Place small cuts of chicken inside, seal bag, and try to combine mixture with the chicken as much as possible. Let rest at room temperature for 30-60 minutes.
In another large Ziploc bag, mix flour, cornmeal, 1 teaspoon salt, 1 teaspoon pepper, and paprika if desired. Remove chicken pieces from the bag, shaking off excess marinade, and place into the flour mixture. Seal bag and shake well until all pieces are covered with flour mixture.
Heat the vegetable oil to 350 degrees F, shake off excess flour, and deep fry chicken in batches. Avoid overcrowding the pan. It will take about 8 minutes (wings and other small pieces) to 12 minutes (drumsticks and other alike pieces). Place fried chicken bites onto a large sheet pan lined with double paper towel to absorb excess oil.
Meanwhile, toast minced garlic with olive oil over medium heat in a small to medium skillet -- just until garlic starts getting lightly brown. Watch carefully! Remove pan from the heat, let cool a bit, and spoon on top of the fried chicken bites. Sprinkle chopped parsley on top and serve by themselves or accompanied by French fries and chilled beer or other drink of your choice.