Toss the shredded zucchini with 1/2 teaspoon salt and let it stand for 15 minutes. Squeeze out as much liquid as possible using a clean kitchen towel.
Drain the cottage cheese in a fine mesh strainer for 15 minutes. Whisk the eggs in a large bowl, then stir in the drained cottage cheese.
Add the zucchini, flour, Parmesan, green onions, dill, garlic powder, baking powder, black pepper, and remaining salt. Stir until a thick, scoopable batter forms.
Heat 1 tablespoon olive oil in a large nonstick skillet over medium heat. Add 1/4-cup portions of batter and gently flatten each portion into a 3-inch fritter.
Cook the fritters for 3 to 4 minutes per side, until deeply golden and cooked through. Repeat with the remaining batter, adding more olive oil between batches as needed.
Stir together the Greek yogurt, lemon juice, lemon zest, dill, and salt. Serve the hot, crisp fritters with the cool lemon dip.