EN
The aim of this paper is to extend the results of Ganikhodjaev et al. to the three state Potts model with competing nearest-neighbor, prolonged next-nearest-neighbor and two-level triple neighbor interactions on a Cayley tree for order 3 and compare with the phase diagrams obtained in Temir et al. and to study modulated phases arising from the frustration effects introduced by nearest-neighbor, prolonged next-nearest-neighbor and two-level triple neighbor interactions.