Does any denomination believe that Jesus left something in writing?

Does any denomination believe that Jesus left something in writing?

The short answer seems to be no with the exception of a possibility in some Eastern Orthodox Churches.

But that does not mean that there may be individuals who believe that such a tradition or legend may exist.

The Abgar legend, according to Christian tradition, posits an alleged correspondence and exchange of letters between Jesus of Nazareth and King Abgar V Ukkāmā of Osroene. In the fourth century Eusebius of Caesarea published two letters which were allegedly discovered in the archives of Edessa. They claim to be an exchange of correspondence between Jesus Christ and King Abgar V which were written during the last years of Jesus' life.

Abgar V was king of Osroene with his capital city at Edessa, a Syrian city in upper Mesopotamia. According to the legend, King Abgar V was stricken with leprosy and had heard of Jesus’ miracles. Acknowledging Jesus' divine mission, Abgar wrote a letter of correspondence to Jesus Christ asking to be cured of his ailment. He then invited Jesus to seek refuge in Edessa as a safe haven from persecution. In his alleged reply, Jesus applauded the king for his faith but turned down the request. He expressed regret that his mission in life precluded him from visiting the city. Jesus blessed Abgar and promised that after he ascended into heaven, one of his disciples would heal all of the illnesses of the king and his subjects in Edessa.

Historical context

Eusebius contains the earliest known account of the Abgar Legend in his first book Ecclesiastical History (ca. 325 C.E.), as part of his discussion of Thaddeus of Edessa. Eusebius claims that Thaddeus went to Abgar at the request of Thomas the Apostle, following Jesus’ resurrection. He also claims to provide the correspondence between Abgar and Jesus, which he translates from Syriac.

Letter of Abgar to Jesus

The church historian Eusebius records that the Edessan archives contained a copy of a correspondence exchanged between Abgar of Edessa and Jesus. The correspondence consisted of Abgar's letter and the answer dictated by Jesus. On August 15, 944, the Church of St. Mary of Blachernae in Constantinople received the letter and the Mandylion. Both relics were then moved to the Church of the Virgin of the Pharos.

A curious growth has arisen from this event, with scholars disputing whether Abgar suffered from gout or from leprosy, whether the correspondence was on parchment or papyrus, and so forth.

The text of the letter was:

Abgar, ruler of Edessa, to Jesus the good physician who has appeared in the country of Jerusalem, greeting. I have heard the reports of you and of your cures as performed by you without medicines or herbs. For it is said that you make the blind to see and the lame to walk, that you cleanse lepers and cast out impure spirits and demons, and that you heal those afflicted with lingering disease, and raise the dead. And having heard all these things concerning you, I have concluded that one of two things must be true: either you are God, and having come down from heaven you do these things, or else you, who does these things, are the son of God. I have therefore written to you to ask you if you would take the trouble to come to me and heal all the ill which I suffer. For I have heard that the Jews are murmuring against you and are plotting to injure you. But I have a very small yet noble city which is great enough for us both.

Jesus gave the messenger the reply to return to Abgar:

Blessed are you who hast believed in me without having seen me. For it is written concerning me, that they who have seen me will not believe in me, and that they who have not seen me will believe and be saved. But in regard to what you have written me, that I should come to you, it is necessary for me to fulfill all things here for which I have been sent, and after I have fulfilled them thus to be taken up again to him that sent me. But after I have been taken up I will send to you one of my disciples, that he may heal your disease and give life to you and yours.

Egeria wrote of the letter in her account of her pilgrimage in Edessa. She read the letter during her stay, and remarked that the copy in Edessa was fuller than the copies in her home (which was likely France).

In addition to the importance it attained in the apocryphal cycle, the correspondence of King Abgar also gained a place in liturgy for some time. The Syriac liturgies commemorate the correspondence of Abgar during Lent. The Celtic liturgy appears to have attached importance to it; the Liber Hymnorum, a manuscript preserved at Trinity College, Dublin (E. 4, 2), gives two collects on the lines of the letter to Abgar. It is even possible that this letter, followed by various prayers, may have formed a minor liturgical office in some Catholic churches.

This event has played an important part in the self-definition of several Eastern churches. Abgar is counted as saint, with feasts on May 11 and October 28 in the Eastern Orthodox Church, August 1 in the Syrian Church, and daily in the Mass of the Armenian Apostolic Church.

Other such pious beliefs are seen with regards to other legendary or traditionally believed writings of Jesus, such as the Copy of a Letter Written by Our Lord Jesus Christ.