For the mayonnaise: In a blender, combine all ingredients and process until smooth. Taste and adjust seasoning as needed. Store covered in the refrigerator until ready to use.
For the fries: Heat oven to 200 degrees F. In a large cast iron skillet, pan, or Dutch oven, heat vegetable oil over medium-high heat to 350 degrees F.
Meanwhile, peel sweet potatoes and cut lengthwise into 1/2-inch planks. Cut planks lengthwise into 1/2-inch strips. Place strips in hot water with vinegar while oil finishes heating. Line a plate with paper towels and set aside.
When oil is heated, drain fries and thoroughly pat dry with paper towels. Add 1/3 of fries to oil and cook until browned and cooked through, about 4 to 5 minutes. Remove fries to paper towels with a slotted spoon and season immediately with kosher salt. Return oil to 350 degrees F and repeat with remaining fries. Hold in oven until fish is ready.
For the fish: Skim oil to clean then return to stove over medium-high and bring to 350 degrees F. Pat fish dry with paper towels then cut into 1/2-inch strips; set aside. In a large bowl whisk together flour, salt, cayenne, and pepper well combined. Add club soda and whisk briefly until a batter is formed (there may be a few lumps left. Place all fish in batter and mix to coat thoroughly. Remove 8 pieces of fish from batter, shake off excess batter, and fry, stirring occasionally, until golden and fish is just cooked through, about 2 to 3 minutes. (To test if fish is cooked, break open 1 piece and make sure meat is white throughout.) Transfer fish with a slotted spoon to paper towels to drain. Return oil to 350 degrees F and repeat with remaining fish. Serve immediately with fries and mayonnaise.