01 - Combine diced chicken, mozzarella, Parmesan, eggs, Greek yogurt, flour, parsley, garlic, salt, pepper, and smoked paprika in a large bowl. Mix until just combined without overworking the mixture.
02 - Pour olive oil into a large nonstick skillet and set over medium heat until shimmering.
03 - Scoop heaping tablespoons of chicken mixture into the hot pan, flattening each portion slightly with a spatula. Cook without overcrowding the pan for 3 to 4 minutes per side until golden brown and cooked through. Transfer finished fritters to paper towels. Add more oil as needed between batches.
04 - Whisk together mayonnaise, lemon juice, garlic, Dijon mustard, parsley, salt, and pepper in a small bowl until completely smooth and creamy.
05 - Arrange warm chicken fritters on a serving plate with the garlic aioli alongside for dipping. Serve immediately while hot.