Make the tartar sauce by stirring together mayonnaise, minced shallots, sweet pickle relish, minced parsley, minced capers, Dijon mustard, lemon juice, granulated sugar, 1/2 teaspoon salt, 2 dashes hot pepper sauce, and black pepper to taste in a small bowl. Cover and refrigerate at least 1 hour.
Set up a breading station: place the flour in one shallow bowl, the lightly beaten eggs in a second, and the panko bread crumbs in a third.
Pat the cod sticks dry and season lightly with salt and pepper.
Working in batches, dredge each cod stick in flour, shaking off excess, dip into the beaten eggs letting excess drip off, then coat evenly with panko. Place breaded sticks on a parchment-lined baking sheet.
If not cooking immediately, wrap the baking sheet and refrigerate up to 1 day, or freeze the sticks on the sheet until solid and transfer to a freezer bag for up to 3 months.
To fry: pour enough vegetable oil into a large skillet to cover the bottom and heat over medium-high until shimmering. Fry the fish sticks in batches without overcrowding, turning so they brown evenly, about 6–8 minutes total per batch.
Transfer cooked fish sticks to a paper towel–lined plate, sprinkle with salt, and serve immediately with the chilled tartar sauce.
Baking alternative: to bake, spray or drizzle prepared sticks with oil and bake in a 450°F oven until cooked through, about 10–12 minutes, turning once to brown both sides.