In a large mixing bowl, whisk together the flour, baking powder, salt, and black pepper. Set aside.
In a separate bowl, combine the beaten egg and milk. Mix well.
Pour the egg and milk mixture into the dry ingredients. Stir until just combined. Do not overmix. The batter will be thick and slightly lumpy.
Add the chopped clams, onion, celery, and parsley to the batter. Gently fold them in until evenly distributed.
In a deep, heavy-bottomed pot or Dutch oven, heat vegetable oil to 350°F (175°C).
Using a spoon or a cookie scoop, carefully drop spoonfuls of the batter into the hot oil. Fry the clam cakes in batches, making sure not to overcrowd the pot. Cook until golden brown and crispy, about 3-4 minutes per side.
Once cooked, remove the clam cakes using a slotted spoon or a spider strainer. Place them on a plate lined with paper towels to drain excess oil.
Serve the Rocky Point clam cakes hot with your favorite dipping sauce, such as tartar sauce or cocktail sauce.