Bring water to boil in medium pot over medium-high heat. Add salt and sugar. Using whisk, slowly whisk in cornmeal. Reduce heat to low. Cook, whisking constantly, until water is absorbed and dough pulls away from pot, 3-5 minutes.
Transfer cornmeal mixture to heat proof bowl; mix in cheese until melted and completely incorporated. Let cornmeal mixture sit until cool enough to handle. Divide dough into 25 equal pieces. Roll each piece into 2½"-3" cigar shape.
Heat 1½" oil in medium, heavy pot over medium-high heat until oil registers 350°F. Fry corn sticks in batches until golden and crisp, about 3-4 minutes per batch; transfer to paper towel to drain. Serve with MayoKetchup.