Season the mackerel with salt and white pepper and arrange the pieces in a 9-by-13-inch glass or ceramic baking dish, skin side down.
In a large saucepan, combine all of the remaining marinade ingredients with 1 1/2 tablespoons of salt and bring to a boil. Reduce the heat to moderately low and simmer until the vegetables are just tender, about 20 minutes. Immediately pour the marinade over the mackerel, spreading the vegetables in an even layer. Cover tightly with plastic wrap and let cool to room temperature, then refrigerate overnight.
Transfer the mackerel fillets to plates, skin side up. Top with some of the vegetables and a drizzle of the marinade; serve the potato salad alongside.
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