Place the grated zucchini in a clean towel and squeeze firmly several times until most of the excess liquid has been removed.
Transfer the zucchini to a bowl and add the corn, eggs, flour, Parmesan, green onions, garlic powder, salt, and pepper.
Stir the mixture until evenly combined and let it stand for about 5 minutes so the flour can absorb any remaining moisture.
Heat one tablespoon of olive oil in a large nonstick skillet over medium heat until the surface is hot but not smoking.
Spoon small portions of batter into the skillet and gently flatten each one into a compact fritter about 1/2 inch thick.
Cook for 3–4 minutes per side until golden brown and cooked through, adding the remaining oil as necessary between batches.
Transfer to a paper towel-lined plate briefly, then serve warm with Greek yogurt, avocado dip, or a squeeze of lemon.