Trim any excess fat from the chicken breasts and dice into roughly 1/3"–1/2" pieces; set aside.
In a medium bowl whisk the eggs with the mayonnaise until smooth, then stir in the flour (or chosen starch), shredded mozzarella, chopped dill, salt, and black pepper until well combined.
Fold the diced chicken into the batter until evenly coated. Cover with plastic wrap and refrigerate to marinate for at least 2 hours or overnight for best texture.
When ready to cook, heat a large nonstick skillet over medium heat and add about 2 Tbsp oil. Once the oil is hot, drop a heaping tablespoon of the chicken mixture into the pan for each fritter (use a flat ice-cream scoop if available) and gently press to flatten slightly.
Sauté the fritters uncovered 3–4 minutes on the first side until golden, then flip and cook 3 minutes more on the second side, or until golden brown and cooked through. Repeat in batches, adding more oil as needed.
Transfer cooked fritters to a paper towel–lined plate to drain briefly before serving.