In a small bowl, whisk together flour, baking powder, and 1/8 teaspoon salt; set aside.
Grate onion on the large holes of a box grater into a medium bowl. Transfer grated onion to a piece of cheese cloth. Squeeze excess liquid from onion and discard. Transfer onion to a clean medium bowl; you should have about 1/2 cup grated onion. Grate zucchini into bowl with onion on the large holes of a box grater; you should have about 3 1/2 cups grated zucchini. Add 1/2 teaspoon salt and toss to combine; let stand 30 seconds.
Transfer zucchini and onion mixture to a clean piece of cheesecloth and cover. Squeeze out as much liquid as possible and discard. Transfer zucchini and onion to a large bowl. Add yogurt and egg; season with salt and pepper. Stir until well combined.
Slowly add 3/4 cup of the flour mixture, while folding it into the zucchini mixture. If mixture seems too wet, fold in 1/4 cup more.
Heat olive oil in a medium skillet over medium-high heat. Working in batches, using about 3 tablespoons of the zucchini mixture, gently form a patty and place in skillet. Cook until fritters are firm and begin to turn golden on the bottom, about 2 minutes. Turn fritters and continue to cook about 2 minutes more. Turn fritters again and cook for 30 seconds; transfer to a paper towel-lined plate. Repeat process with remaining zucchini mixture, adding more oil as necessary.
Season fritters with salt and serve immediately with yogurt-dill sauce.