Soak the black-eyed peas overnight in cold water to cover. Drain. Rub off and discard the skins. Soak the shrimp in cold water to cover for 30 minutes. Puree the peas, onion, shrimp, garlic and cayenne in a food processor. Season to taste with salt, if necessary. Form mixture into tablespoon size balls.
Meanwhile in a 5-quart pot or Dutch oven, fitted with a candy or deep-frying thermometer, or in an electric deep fryer, heat oil over medium-low heat until the thermometer registers 365 degrees F. Make sure you have at least 3 inches of space between the top of the oil and the top of the pan, as oil will bubble up when fritters are added.
Fry the fritters in small batches until golden brown all over, turning once. Remove with a slotted spoon and drain on paper towels. Serve at room temperature with Black-eyed Pea Fritter Sauce.
Yield: about 2 dozen