Combine the mayonnaise, 1/4 cup parsley, dill, pickles and capers in a medium bowl. Stir in the juice from 1/2 lemon, check seasoning and add salt and pepper if necessary. Set the sauce aside.
Combine the flour and a pinch of salt in a shallow or medium bowl. Beat the eggs in a separate shallow bowl. Combine the panko, cheese, remaining 1/4 cup parsley and the zest from 1 lemon in another shallow bowl. This is your breading station.
Dredge the cod strips in flour, followed by the egg and finishing with the breadcrumb mixture.
Heat the oil in a medium (10-inch) straight-sided pan or skillet until hot, 350 to 360 degrees F. Add the fish sticks and shallow-fry, turning so they brown evenly, 4 to 6 minutes total.
Drain the fish sticks on a paper towel-lined plate or wire rack and season with salt. Serve with the sauce and lemon wedges.