In a bowl, combine the finely grated zucchini and salt, stirring well. Set aside for 10 minutes to allow the salt to draw out excess moisture.
Place the zucchini mixture onto a clean dish towel or cheesecloth, then squeeze firmly to drain out all the liquid.
In a separate bowl, whisk the egg, then add the all-purpose flour, Parmesan cheese, salt, and ground black pepper. Stir until well combined.
Add the drained zucchini to the batter and mix thoroughly.
Heat oil in a medium-sized pan over medium-high heat.
Spoon the batter into the hot oil, approximately one tablespoon at a time, shaping each spoonful into a fritter. Cook until golden brown on both sides, about 5 minutes per batch.
Once cooked, transfer the fritters to a serving plate. Sprinkle with grated Parmesan cheese and a pinch of salt.
Serve the fritters immediately with a dollop of sour cream on top.
