Place clams, artichokes, cherry peppers, and lemon slices in a large mixing bowl.
Pour milk over the mix, then place in refrigerator for 1 hour to marinate.
While clam mix is marinating, make preserved lemon and dill mayonnaise.
Using a small fryolator or Dutch oven, carefully heat the oil to 350°. Maintain this temperature.
Remove clam mix from the refrigerator; strain off milk and discard.
In a medium bowl, whisk cornstarch and flour together until combined.
Working in batches, dredge the clams, artichokes, cherry peppers, and sliced lemons into the cornstarch & flour mixture; shake off any excess flour mixture and carefully drop into the hot oil.
Fry the ingredients until crispy and cooked through. Remove cooked ingredients from oil and place on paper towel to soak up excess oil.
Season hot ingredients with salt and black pepper.
Spread some preserved lemon and dill mayonnaise on inside of rolls. Stuff the rolls with equal amounts of crispy fried clams, artichokes, cherry peppers, and lemon slices.
Garnish with extra dill and serve warm.