Do you mean is there Byzantine Chant in the Turkish language? Or are you asking if there is a parallel musical system to BM in Turkish music history?
To the former question - Im not at all sure if there is and I would actually be surprised if indeed there is. I an under the assumption that Orthodox worship in Turkey is done in the Greek language - that is that the Orthodox churches in existance there use the Greek language or at least the ones I visited did. Perhaps there are some musicians that have composed chant to suit worship in the Turkish language? Or perhaps translations exist? Maybe someone can enlighten me or point me in the right direction with this.
To the latter question I would say yes, that there are parallels to some extent. But again I am not well read enough on this topic to provide examples. I will endeavour to find out more however.