Grate the zucchini and squeeze out as much liquid as possible using your hands or a cheesecloth. Set the zucchini aside in a medium-sized bowl.
Finely chop the small onion and add it with the grated zucchini.
Add the egg, yogurt and season with salt and pepper. Whisk well until combined.
Stir in the flour and baking powder until combined. The mixture will seem a little thick at first, but once you let it sit for 10 minutes, some of the moisture from the zucchini will come out and it will be perfect for cooking.
Heat up the vegetable oil in a medium skillet over medium-high heat. Working in batches, drop about 2 tablespoons of the zucchini mixture in the skillet. Cook until the fritters are firm and golden brown on the bottom. Flip the fritter overs and cook for an additional 2 minutes or so.
Transfer the fritters to a paper-towel lined plate to drain any oil.