For the fish sticks: Heat about an inch of oil in a heavy saucepan over medium-high heat until a deep-fry thermometer inserted in the oil registers 360 degrees F.
Heavily sprinkle the fish sticks on both sides with salt and pepper. Form an assembly line with the flour, whisked eggs and panko breadcrumbs in separate shallow bowls. Dredge the fish sticks first in the flour, making sure to remove any excess, then in the egg wash and finally in the panko.
Fry the fish until golden in color, about 3 minutes per side. Set on a paper towel to drain the excess oil.
For the tartar sauce: Place the mayonnaise, chopped pickles, capers, white wine vinegar and grain mustard in a blender and process until smooth. Serve with the fish sticks.