Karaim-Karaylar are an Unitarian Mosaic Clergy who constitute the priesthood for the original Karaim Noachite base of the Molokans and Sabbatarians. The Karaim-Karaylar and their off-shoots have a history of attraction to Rabbinical practice although they are usually confused on the contrary with Karaite Jews with whom they share nothing but a name in common.

As the early Christian Churches emerged in late antiquity, one by one they cut themselves off from the Unitarian Mosaic Clergy. The first to do so was Sylvester the Bishop of Rome in 318CE followed by Emperor Constantine who passed such harsh legislation against them in 333CE that in 345CE many were forced to emigrate to Kerala. The Nestorian Church first distinguished the Unitarian Mosaic Clergy as Apostates (Hunefa) during the reign of Khosrau II Parviz (22nd Sassanid King of Persia 590-628CE) for rejecting the election of Nestorian Catholicos Gregorius of Seleucia. Gregory responded against the Unitarian Mosaic Clergy by sending Babai the Great who evicted them from the Monastery of mount Izla in Nisibis driving them into the Arabian desert.

In the desert they found refuge with Nestorian converts among the Quraish (the most famous of whom at this time being Waraka ibn Naufal and Khadijah) who also rejected the election of Gregory as Catholicos. Here, Abu Qasim was established over them as His Grace "Mahomed" ("Most Graceful") Bishop Mustapha ibn Abdullah, and many other Nestorians like Salmān e Pārsī joined the protest movement in the desert.

See also Unitarian Universalism