Place the shredded zucchini in a colander set over a bowl and sprinkle the zucchini lightly with salt. Allow the zucchini to stand for 10 minutes. Using your hands, squeeze out as much liquid from the zucchini as possible. Transfer the zucchini to a large bowl.
Add the flour, eggs, sliced scallions, 1/4 teaspoon salt and 1/8 teaspoon pepper to the bowl, stirring until the mixture is combined. Line a plate with paper towels.
Add the olive oil to large sauté pan set over medium heat. Once the oil is hot, scoop 3-tablespoon mounds of the zucchini mixture into the pan, pressing them lightly into rounds and spacing them at least 2 inches apart. Cook the zucchini fritters for 2 to 3 minutes, then flip them once and cook an additional 2 minutes until golden brown and cooked throughout. Transfer the zucchini fritters to the paper towel-lined plate and immediately sprinkle them with salt. Repeat the scooping and cooking process with the remaining zucchini mixture.
Serve the zucchini fritters topped with sour cream (optional) and sliced scallions.