Grate the telemea cheese on the large holes of a box grater into a medium bowl.
Add the egg to the bowl with the grated cheese.
Sprinkle in the tablespoon of sugar and mix briefly to combine.
Pour in the water and stir until the mixture loosens slightly.
Add the flour, mixing first with a spoon, then switching to your hands as the dough starts to come together.
Knead the dough just until it comes together and feels slightly sticky but holds its shape.
Pinch off small pieces of dough and roll them into balls, dusting them lightly with flour. Then use the rim of a glass to press and shape each ball into a neat round. Place the glass over the dough ball and rotate it a few times to smooth the edges.
Repeat with the remaining dough; you should get about 12 dough balls.
Pour a shallow layer of oil into a frying pan, set it over medium-low heat, and let the oil heat for about a minute. Gently transfer the cheese fritters to the pan, cover with a lid, and fry over low heat.
After a few minutes, flip each fritter to the other side and continue frying until golden.
The savory papanasi are ready when golden and cooked through; serve hot and enjoy.