West Asia
Asu-shu-namir: queer hero of Akkadian myth
From Sumerian mythology: the non-binary agents who saved the Queen of Heaven
Enkidu and Gilgamesh – homoromantic soulmates
South Asia
King Bhagiratha, born of two mothers, brings the Ganges down from the heavens
Check out Devdutt Pattanaik’s book Man Who Was A Woman: And Other Queer Tales from Hindu Lore