For the teriyaki sauce: Combine the soy sauce, mirin, sake and sugar in a bowl. Add the mixture to a large nonstick skillet and bring to a light simmer over medium heat, stirring gently, until the sugar is dissolved. Remove from the heat. Transfer to a bowl and set aside to let cool. Wipe out the skillet with a paper towel.
For the salmon: Sprinkle each salmon fillet with salt and pepper. Put the potato starch in a bowl and season with salt and pepper. Lightly dust each fillet with potato flour all over.
Set a skillet over high heat until hot, then add the oil. Add the salmon and fry each side until golden brown all over, 3 to 4 minutes total. Remove the salmon to a plate.
Add 1/2 cup of the teriyaki sauce to the skillet. Transfer the remaining sauce to an airtight container and reserve for another use; the sauce will keep up to 3 weeks in the refrigerator. Bring the sauce in the skillet to a boil over medium heat, then immediately reduce the heat and bring to a simmer. Cook until the sauce is reduced by half then return the salmon to the skillet and warm through. Turn off the heat and spoon the sauce over the salmon.