A blessed Nativity / Theophany season to all!
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Good question. It sounds like there is major Eastern Christian history, but that it got taken over by Catholicism:
Records suggest that St. Thomas Christians and Nestorian Christians lived in Sri Lanka. Anuradhapura cross (https://en.wikipedia.org/wiki/Anuradhapura_cross) is one of the archaeological claims that suggest Christianity in Sri Lanka before Portuguese.
The Syriac Orthodox Church is in the process of trying to revive the Church there.
Besides the ancient historical Church, there was a mission based out of Malankara in the late 19th early 20th century, authorized by the then Patriarch. Unfortunately, with the schism in Malankara, this community fell into disarray.