Microwave shredded carrot 30 seconds to soften, then set aside. In a medium bowl, combine baking mix, cornmeal, and sugar. Stir in milk and egg, and mix well. Stir in corn, zucchini, and shredded carrot.
In a skillet, heat 1/3 inch of oil to 375°F. Gently spoon dollops of fritter mixture into oil and fry, turning once, until golden brown and cooked through, about 4 minutes. Drain on paper towels, serve warm.