In a bowl, combine the shredded squash and potatoes with the cornstarch, eggs and onion and season with salt and cayenne. In a large nonstick skillet, heat 1/8 inch of oil until shimmering. Add 2-tablespoon-size mounds of the mixture to the skillet and cook over moderate heat, turning once, until golden and cooked through, 4 to 5 minutes. Drain on paper towels and repeat, adding more oil to the skillet as needed and wiping out the pan occasionally. Top the rösti cakes with sour cream, caviar and chives and serve hot.