For teriyaki sauce, combine ingredients in a small saucepan, bring to the boil over medium heat and simmer until sugar is dissolved (2-3 minutes), set aside. Teriyaki sauce will keep refrigerated in an airtight container for 1 month.
Heat oil in a large frying pan over medium-high heat, add quail in batches, skin-side down, and cook, turning once, until golden (2-3 minutes each side). Return quail to pan, add teriyaki sauce and simmer until slightly thickened (3-4 minutes). Scatter with chives and sesame seeds and serve hot with steamed rice.