For the Gullah seasoning: Combine the paprika, salt, basil, garlic powder, onion powder, oregano, white pepper, thyme, sugar and cayenne in a paper bag and shake to mix up well.
For the shrimp: Line a baking sheet with butcher or parchment paper. Pour the buttermilk in a bowl.
Mix together the flour and 1 1/2 tablespoons Gullah seasoning in a bowl (reserve the remaining seasoning for another use).
Dip the shrimp in the buttermilk, then dredge in the flour mixture, shaking the bag to coat. Shake off the excess flour and place on the prepared baking sheet. Discard the buttermilk mixture but reserve the flour mixture.
Place the oil in a Dutch oven or heavy pan and heat to 350 degrees F. Line a baking sheet with paper towels and set a wire rack on top.
Fry half the shrimp until golden brown, 1 to 2 minutes per side. Remove to the prepared wire rack to drain. Repeat with the remaining shrimp.
Reduce the heat of the oil to 325 degrees F. Line a baking sheet with paper towels and set a wire rack on top.
For Mom's fries: Slice the potatoes into 1/2-inch-wide sticks. Add the potatoes to the flour mixture and shake until the potatoes are coated. Drop a few in the oil. Fry in batches until golden brown, flipping and stirring frequently, 7 to 10 minutes. Remove to the prepared wire rack to drain in a single layer.
For the fry sauce (if using): Whisk together the mayonnaise, ketchup, pickle relish, dill and hot sauce in a medium bowl. Transfer to a serving dish and serve alongside the fries and shrimp.