Combine water, butter, salt, and 1/4 teaspoon cinnamon in a 1 1/2-quart saucepan over medium heat and bring to a rolling boil.
Reduce heat to low. Add flour and stir vigorously until the mixture forms a ball. Remove from heat and rest 5 to 7 minutes.
Add eggs one at a time, stirring until combined.
Heat oil in a medium skillet or 1-quart saucepan to 350°F.
Spoon dough into a piping bag fitted with a large star tip. Pipe 1-inch strips over the pan, cut with a knife, and drop into the hot oil without overcrowding.
Fry until golden brown, remove with a slotted spoon or spider, and drain on paper towels.
Mix sugar with the remaining 1/2 teaspoon cinnamon. Toss warm churro bites in cinnamon sugar and serve with your favorite dipping sauce.