Char the red pepper directly over a gas flame or under the broiler, turning frequently, until blackened and blistered on all sides. Transfer the pepper to a plate to cool for about 10 minutes. Discard the blackened skin, stem and seeds and cut the pepper into 1/4-inch dice.
In a large bowl, whisk the flour with the cornmeal, baking powder, 3/4 teaspoon of salt and 1/4 teaspoon of pepper. Stir in the milk and egg. Fold in the crabmeat, corn kernels, scallion and diced red pepper. Let the batter rest for 10 minutes.
In a small bowl, blend the mayonnaise with the basil, cilantro, lemon juice, tarragon and mustard and season with salt and pepper.
Preheat the oven to 300°. Have ready a rack set over a baking sheet. In a large skillet, heat 1 1/2 inches of oil to 350°. Cook the beignets without crowding the pan: Drop rounded teaspoons of the batter into the hot oil and fry until golden, about 1 minute per side. Drain on the rack and keep warm in the oven while you fry the rest. Repeat with the remaining batter, adjusting the heat if the beignets brown too quickly. Transfer the beignets to a platter and serve with the herbed mayonnaise.
The batter and the mayonnaise can be refrigerated overnight.