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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.[5] Anuradhapura cross (https://en.wikipedia.org/wiki/Anuradhapura_cross) is one of the archaeological claims that suggest Christianity in Sri Lanka before[6] Portuguese.
https://en.wikipedia.org/wiki/Christianity_in_Sri_Lanka
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.