Pat the chicken pieces dry and line a baking sheet with wax paper. In a large bowl, whisk the eggs with the milk. Add the chicken. In another bowl, whisk the flour with the seasoned salt and seasoned pepper. Dredge the chicken in the seasoned flour and transfer to the baking sheet.
In a 12-inch, cast-iron skillet, heat the vegetable shortening to 365°. Add all of the chicken and fry over moderate heat, turning occasionally, until deeply golden brown and an instant-read thermometer inserted nearest the bone registers 170°, 20 to 24 minutes. Drain the chicken on paper towels and serve right away.