Mar Shemÿon III was the patriarch of the Church of the East in the early 15th century. There is uncertainty over his existence, his dates and his place in the order of patriarchs.
Traditionally, Shemÿon III is listed between patriarchs Shemÿon II, whose reign began in 1381/2, and Eliya IV, who is said to have died in 1437. A manuscript made in the reign of the Shemÿon who succeeded Eliya IV casts doubt on this reconstruction, however. In a copy of the Book of the Bee, a list of patriarchs has been extended from the time of Timothy II to "Shemÿon of our days". The intervening patriarchs are Denha II, a certain Shemÿon and Eliya IV. This can only be Shemÿon II.
Manuscript colophons from 1429/30 and 1437 attest to a patriarch named Shemÿon, and David Wilmshurst suggests that this person, along with the "Shemÿon of our days" of the Bee manuscript, was Shemÿon III, who succeeded Eliya IV around 1425. He dates his patriarchate from c. 1425 to c. 1450. Jean Maurice Fiey went so far as to deny the existence of Shemÿon III entirely. This would give Shemÿon IV (successor of Eliya IV or Shemÿon III, depending on the list) a reign of sixty years or more.