Otherwise attested in this precise form only in the scholia to Lycophron, Alexandra line 174 (where Medea is called 'Kytaike'). The scholiast asserts that Kyte is a city in Kolchis (present-day Georgia).
This gives rise to 2 possible identifications. If the Kolchian city is meant, it is probably Kotais/Kytaia (kappa 2788), present-day Kutaisi in Georgia. See Barrington Atlas map 88, grid A2. But there was also a city near Zavetnoye in the present-day Ukraine which was known in antiquity by the names Kytai/Kydeake/Kyta/Kytaion (kappa 2789). See Barrington Atlas map 87, inset.