That unexplained epithet is the seed of a large body of later writing, none of which is by him.
The Gospel of Thomas, recovered complete in Coptic at Nag Hammadi in 1945 with Greek fragments long known from Oxyrhynchus, is a collection of one hundred and fourteen sayings with no narrative, no passion and no resurrection. Its opening line attributes it to Didymos Judas Thomas. Dating is contested along a wide range: some scholars place a core in the first century, potentially independent of the canonical Gospels, while others date the collection as we have it to the mid second century and read it as dependent on them. Both positions are held by serious people and the question is not settled.
The Acts of Thomas, a third-century Syriac romance, makes the twin explicit and startling: Thomas is the twin brother of Jesus. It also supplies the narrative of his mission to India, his conversion of a king named Gundaphorus, and his death by spearing near Mylapore. A king of that name is real, Gondophares, an Indo-Parthian ruler of the first century, is attested on coins and in an inscription, which is a genuine and unexpected point of contact, though it establishes only that the author knew a real name.
The Saint Thomas Christians of Kerala are an ancient community, and Christianity in south India is attested well before European contact. Their tradition of apostolic foundation by Thomas in 52 CE is central to their identity and is not archaeologically demonstrable. What can be said is that the community is old, the claim is old, and the evidence does not extend to the first century.