Place the grated zucchini in a colander over the sink and sprinkle with 1 teaspoon of salt. Gently toss to combine and allow it to sit for 10 minutes.
Afterward, use a clean dish towel or cheese cloth to drain the zucchini thoroughly.
In a large bowl, combine the zucchini, chicken, mozzarella, corn, Parmesan, flour, egg, chives, lemon zest, and garlic. Season with salt and pepper to taste, mixing until well incorporated.
Heat vegetable oil in a large cast iron skillet over medium-high heat. Working in batches, scoop 3-4 tablespoons of the batter for each fritter, flattening them with a spatula.
Cook the fritters until the underside is golden brown, about 2-3 minutes. Flip and cook for another 2 minutes, or until golden brown on the other side.
Serve the fritters immediately with the sour cream sauce.
For the sour cream sauce, combine the sour cream, chives, lemon juice, and garlic in a medium bowl.
Season with salt and pepper to taste. Refrigerate until ready to serve.