To make the dough: Place the flour, sugar and salt in a food processor. Add the butter and water until a dough forms.
Form a ball, cover with plastic wrap and place in the refrigerator for about 40 minutes.
On a lightly floured surface, roll out the dough into a thin rectangle.
With a pizza cutter or sharp knife, cut dough into strips about three times the size of the cheese sticks.
Wrap the cheese stick using one strip of dough overlapping the dough. Fold and seal the edges.
Repeat this process with the remaining cheese and dough. Cover and freeze until frozen, about 2 hours and up to 2 days.
Heat the oil in a large frying pan over medium heat. Working in batches, fry the cheese sticks until golden brown, about 1 minute per side. Transfer the palitos de queso to a plate lined with paper towel and eat immediately.