Simmer the potatoes in a generous amount of cold water until very tender, and then drain. Set potatoes back on the heat for a minute to evaporate any water in the bottom of the pot. Remove from the heat, and then thoroughly mash potatoes. Spoon potatoes into a bowl and cool to room temperature.
Cut cod into thin, lengthwise strips, removing any bones you find. Now cut each strip into small, 1/4" to 1/2" cubes. Add the fish to the potatoes, along with the corn, onion, egg, mustard, tarragon, flour, salt and pepper. Mix well to combine.
Spread the breadcrumbs on a wide plate. Dampen your hands slightly with cold water. Divide and shape the fish mixture into 8 even balls. Shape each ball into 3-inch wide cake. Coat cakes in breadcrumbs, gently pressing them on to help them adhere, and then set cakes on a baking sheet.
Divide the oil between 2, 10" non-stick skillets set over medium, medium-high heat. When hot, fry cakes until golden brown and the fish is cooked through, about 4 minutes per side.
Set 2 fish cakes on each of four plates. Garnish each plate with 2 half lemon slices and serve.
Note: One large cob of corn should yield the amount required for this recipe. Use a sharp paring knife to cut the kernels off the cob.