This question is inspired by this post and the resulting discussion: https://reddit.com/r/MapPorn/comments/m7tiq6/what_happened_to_the_disciples_oc/
I’m familiar with the St. Thomas legend that he came to the Malabar Coast to proselytize and spread Christianity, but I’m not sure if there are any records of this actually happening, or if it’s reasonable to expect there to be records from this time period.
I’m also familiar with the ancient Jewish population that existed in Cochin, India. According to Wikipedia, they seem to have arrived in Kerala centuries earlier according to the Wikipedia post: https://en.wikipedia.org/wiki/Cochin_Jews?wprov=sfti1
Kerala has a long history of Christianity which dates back to the legend of St. Thomas. I can't answer any questions directly on that as my knowledge comes from the Anglican side. What is known is that most of the early Christian churches had entered a severe decline by 1400 AD, from a perfect storm of persecution, disease, and isolation.
The Governor General of British East India Company requested assistance to convert the local populace and in response the first Church Missionary Society missionary to Kerala, India was Thomas Norton sent in 1816. He founded a mission station and school in Allepie, then two years later finished construction of his church. Numerous records and letters from him and his wives exist (he is a distant ancestor of mine) and we were able to donate them to the CMS. I'll leave the more personal anecdotes out as they are fairly controversial. He was joined by Joseph Fenn, Henry Baker and Rev. Benjamin Bailey in 1821 who not only created the first typescript for the Malayalam language but translated the Bible into Malayalam.
After a while, it became difficult to reconcile the differences between the Eastern Orthodox that were practised by the established churches and the Anglican Christianity which were promoting at the time so there was a schism.
I recommend reading Thomas Norton: Man on a Mission for more information on the Anglican side, or Seasickness and Prayers which contains a lot of information from his wives letters and diaries.
I will rely on others to provide further information for the Eastern Orthodox Churchs, that pre-date the Anglican church and will close to say that they are rather ironically now sending missionaries to the UK.
References:
Thomas Norton: Man on a Mission by Gillian Mary Webb
Seasickness and Prayers by Gillian Mary Webb