Peyia is already a town within the Paphos district...one of the areas is Peyia village, along with Coral Bay and Sea Caves to name a couple.
"Peyia is a town in the Paphos District of Cyprus. Pegeia is situated mainly on the steep slopes of the coastal hills inland from Coral Bay, at the southern end of the Akamas Peninsula, and it lies 14 km northwest of Paphos. It has a large British population and a growing number of holiday homes and apartments."
https://www.google.com/maps/place/Peyia/@34.8942407,32.3636037,13z/data=!3m1!4b1!4m5!3m4!1s0x14e7a7839a5077e3:0xcbfbeff844499f3c!8m2!3d34.8833497!4d32.3874598