Preheat the oven to 400°F. Place the fish on a foil or parchment-lined baking sheet and season with dill weed, salt and pepper. Bake until cooked through about 6–8 minutes. Let cool and flake into small pieces using a fork.
While the fish is cooking, place the potatoes in a medium saucepan and fill with cold water. Season with salt and bring the water to a boil, cooking the potato until it’s fork tender. Drain the potato and allow to it cool before mashing with a fork.
In a mixing bowl, combine the fish, potato, egg, parsley, lemon zest and mayonnaise. Using damp hands, shape the mixture into 8 patties. Place the patties on a plate or baking sheet and chill for at least 30 minutes. This will help the fish cakes to firm up.
While the fish cakes are chilling make the dipping sauce. Whisk together the yogurt, mayonnaise, salt and lemon juice. Add the minced pickles and stir to combine.
Heat the oil in a skillet set over medium heat. Coat the patties evenly with the breadcrumbs and fry them in batches of 4, cooking until the outsides are golden brown, about 4 minutes per side. Serve with dipping sauce.