In a large bowl, stir the potatoes, turkey, and sweet potatoes until well-mixed. Form into 1 1/2-inch balls. Roll in the panko crumbs until well coated, pressing the crumbs to adhere.
Fill a medium saucepan with oil to a depth of 3 inches. Heat the oil until hot but not smoking (360°F). Carefully add about 5 balls; do not crowd the pan. Cook, turning once, until golden brown and heated through, about 3 minutes. Transfer the balls to paper towels.
Repeat with the remaining balls, reheating the oil between batches.