In a large mixing bowl, combine the flour, salt, and sugar.
Add the chilled butter and use your fingers or a pastry cutter to work it into the flour until the mixture resembles coarse crumbs.
In a separate bowl, whisk together the egg and water.
Gradually add the egg mixture to the flour mixture, stirring until a dough forms.
Knead the dough on a lightly floured surface for about 5 minutes, or until smooth and elastic.
Wrap the dough in plastic wrap and refrigerate for at least 30 minutes.
Cut the queso blanco or mozzarella cheese into sticks about 3 inches (7.5 cm) long and 1/2 inch (1.25 cm) thick.
On a lightly floured surface, roll out the dough to about 1/8 inch (3 mm) thickness.
Cut the dough into long strips about 1 inch (2.5 cm) wide.
Take one cheese stick and wrap a dough strip around it, starting at one end and spiraling to the other end, overlapping slightly. Make sure the cheese is fully enclosed by the dough.
Press the edges of the dough to seal.
Repeat with the remaining cheese sticks and dough strips.
In a large skillet or deep fryer, heat vegetable oil to 350°F (175°C).
Fry the tequeños in batches until golden brown and crispy, about 3-4 minutes per side.
Use a slotted spoon to remove the tequeños from the oil and drain on paper towels.
Enjoy your meal!