Byzantine version of Cossacks/Moriscos/Mudéjares?

Deleted member 97083

In a late Byzantine restoration scenario where Anatolia has already been Turkified, but Constantinople retakes parts of Asia Minor, what would be the Byzantine analogue to Iberian Moriscos and Mudéjares or Russian Cossacks?

Also, if large numbers of Turks converted to Orthodoxy, would the Greek peasantry eventually start speaking Turkish due to the Byzantine and Ottoman policies of population movement and settlement between core and periphery regions?
 
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