Combine the soy sauce, vinegar, water, sesame oil, ginger, and garlic in a shallow dish just large enough to hold the salmon and mix well. Add the salmon, cover with plastic wrap, and refrigerate for one hour, turning once.
Remove the salmon from the marinade and brush off as much marinade as possible. Heat a large nonstick skillet over medium-high heat. When the pan is hot, add the salmon skin-side up. Cook until the bottom has darkened and the sides become opaque, 3 to 5 minutes. Flip, and cook until the bottom has darkened and the fish is just cooked through, 3 to 5 minutes longer. Transfer the fish to a platter and top with the scallions and sesame seeds.