The story of how King Abgar and Jesus had corresponded was first recounted in the 4th century by the church historian Eusebius of Caesarea in his Ecclesiastical History. (i.13 and iii.1) and it was retold in elaborated form by Ephrem the Syrian.
In the origin of the legend, Eusebius had been shown documents purporting to contain the official correspondence that passed between Abgar and Jesus, and he was well enough convinced by their authenticity to quote them extensively in his ecclesiastical history. By the time the legend had returned to Syria, the purported site of the miraculous image, it had been embroidered into a tissue of miraculous happenings (Bauer 1971, ch. i): the Doctrine of Addai is full of miracles. Some people consider it to be filled with anti-semitism in the story of "Protonice" consort of Claudius, searching for the Cross, and Golgotha and the Holy Sepuchre, all of them in possession of the Jews.