Bring water to a boil in a saucepan and stir in sugar, butter, and salt until sugar has dissolved. Turn heat to low and whisk in 1 cup of cornmeal until smooth. Stir in remaining 1/2 cup cornmeal to make a very thick, workable dough.
Heat 3 cups vegetable oil in a deep-fryer or large saucepan to 350 degrees F (175 degrees C). Grease your hands well with 2 teaspoons of oil and scoop about 3 tablespoons of cornmeal dough; roll the dough into a ball, then shape into a 3-inch long stick about 1/2 inch wide. Repeat with remaining dough, oiling your hands as needed. Deep-fry the cornmeal sticks until golden brown, working in batches of 3 or 4 at a time. Drain fried cornmeal sticks on paper towels and keep warm.
Mix mayonnaise, ketchup, and garlic salt in a bowl until well combined; serve cornmeal sticks with the sauce for dipping.