Α Medieval Roman church with a weird architecture in Cyprus

Well Yes! That's a Byzantine church. It's called Panaghia Arakiotissa. In Byzantine times it was called Virgin of Arakos. The church is situated on the Troodos mountain range. It's a Unesco World heritage site.

It's dated back to the age of the Comnenian dynasty. It served as the main church building of a monastery. It was an era of insecurity for the island as the crusaders had set their eyes on Cyprus and the local Byzantine lords had conflicts with the Constantinopolitan authorities.

The Virgin of Arakas. Made by a famous Byzantine hagiographer. Theodore Apsevdis

Apart from its cultural value as a building, the church features some impressive Byzantine mural in the interior. Many of them had been painted by the famous hagiographer, Theodore Apsevdis.