Combine zucchini, carrots, corn, chives and garlic in a large bowl. In a small bowl, whisk the eggs and Greek yogurt together. Combine with the veggies.
In a separate bowl, combine the flour, cornmeal, baking powder, salt and pepper. Add it to the veggies. Fold in the cheese.
Heat olive oil in a skillet. Form balls of about 2 tablespoons of dough at a time. Add to skillet and press flat with the back of your spatula to form a fritter shape. Cook on both sides until golden brown. Remove from your skillet onto a cooling rack with a piece of paper towel on top. Serve warm with a dollop of Greek yogurt and a sprinkle of chives on top.