Grate the zucchini on the fine holes of a box grater or in a food processor. Transfer to a bowl and squeeze firmly to remove excess liquid.
Combine the onion, dill, parsley, zucchini, garlic, salt, pepper, flour, and egg in a large bowl. Mix until just combined. Fold in the feta and provolone. Cover and refrigerate for 30 minutes to firm.
Heat oil in a wide skillet over medium-high heat. Scoop heaping tablespoons of batter into the oil, spacing evenly. Fry until deeply golden, 2 to 3 minutes per side. Transfer to a rack to drain.
Stir the yogurt, dill, cucumber, garlic, lemon juice, and salt until smooth. Adjust seasoning to taste. Serve fritters hot with tzatziki alongside.