Place grated zucchini, carrots, and onion in a tea towel or several paper towels and wring out as much liquid as possible. Mix together the remaining ingredients. Heat about 2-3 tbsp vegetable oil in a large pan/skillet on medium-high heat.
Working in batches, use your hands to scoop out some fritter mix, shape into tight balls, place in hot skillet, and flatten with the back of a spatula. Once each fritter is crispy and golden on both sides, remove and let dry on paper towels.
For the dipping sauce, combine yogurt, garlic, and cilantro in a food processor and blend until smooth.