There is quite a bit of tradition and evidence supporting that. The following is from Wiki:
According to traditional accounts of the Saint Thomas Christians of modern-day states of Tamil Nadu and Kerala in India, Saint Thomas travelled outside the Roman Empire to preach the Gospel, travelling as far as the Tamilakam which is in South India, Tamil Nadu, India[1][4][5][6] and reached Muziris of Tamilakam (modern-day North Paravur and Kodungalloor in Kerala State, India) in AD 52.[7][8][1] In 1258, some of the relics were brought to Ortona, in Abruzzo, Italy, where they have been held in the Church of Saint Thomas the Apostle.[9] He is regarded as the patron saint of India among its Christian adherents,[10][11] and the Feast of Saint Thomas on July 3 is celebrated as Indian Christians' Day.[12][13] The name Thomas remains quite popular among the Saint Thomas Christians of the Indian subcontinent.
Many churches in the Middle East and southern Asia, besides India, also mention Apostle Thomas in their historical traditions as being the first evangelist to establish those churches, the Assyrian Church of the East,[14] the early church of Sri Lanka.[15]
According to traditional accounts of the Saint Thomas Christians of modern-day states of Tamil Nadu and Kerala in India, Saint Thomas travelled outside the Roman Empire to preach the Gospel, travelling as far as the Tamilakam which is in South India, Tamil Nadu, India[1][4][5][6] and reached Muziris of Tamilakam (modern-day North Paravur and Kodungalloor in Kerala State, India) in AD 52.[7][8][1] In 1258, some of the relics were brought to Ortona, in Abruzzo, Italy, where they have been held in the Church of Saint Thomas the Apostle.[9] He is regarded as the patron saint of India among its Christian adherents,[10][11] and the Feast of Saint Thomas on July 3 is celebrated as Indian Christians' Day.[12][13] The name Thomas remains quite popular among the Saint Thomas Christians of the Indian subcontinent.
Many churches in the Middle East and southern Asia, besides India, also mention Apostle Thomas in their historical traditions as being the first evangelist to establish those churches, the Assyrian Church of the East,[14] the early church of Sri Lanka.[15]