Combine potatoes, potato starch, scallions, chiles, eggs, salt, and pepper in a large bowl, stirring until well blended.
Heat 1/4 cup oil in a large nonstick skillet over medium-high until shimmering. Spoon 8 (2-tablespoon) portions into skillet, flattening each portion into a 1 1/2-inch disk. Cook until crisp, about 4 minutes. Turn and cook until crisp, 3 to 4 more minutes. Drain on paper towels. Keep latkes warm in a single layer on a baking sheet in a 175°F oven. Repeat process twice with remaining oil and potato mixture.
Place warm latkes on a serving platter. Top each with 1 teaspoon sour cream and 1/2 teaspoon tobiko. Sprinkle with chives.