Pat shrimp dry with paper towels then dice into pea-sized pieces.
Transfer chopped shrimp to a large mixing bowl. Add 4 oz shredded mozzarella, 1 egg, 1/4 cup mayo, 2 Tbsp parsley, 1/2 tsp salt and 1/8 tsp black pepper. Stir together then add 1/4 cup flour and mix until batter is creamy and well combined.
Heat a large non-stick pan over medium heat and add 1 Tbsp olive oil. Add 1 heaping Tablespoon at a time (or a level ice cream scoop) and flatten out the tops of your fritters as you go so they are about 1/2" thick patties. Saute about 3 minutes per side or until golden brown on the edges and cooked through.
Alternatively, place them in muffin tins sprayed with cooking spray, and bake in preheated 350F oven for 20-30 minutes, checking for doneness after 20 minutes.
Lemon Aioli Sauce:
In a small bowl, add mayo and stir to remove any lumps. Add 1 tsp lemon zest, 2 Tbsp lemon juice and pressed garlic clove and stir to combine.