By controlling the vortex core energy, the three-state ferromagnetic Potts model can exhibit two types of topological paradigms, including the quasi-long-range ordered phase and the vortex lattice phase [Phys. Rev. Lett. 116, 097206 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.097206]. Here, using Monte Carlo simulations using an efficient worm algorithm, we show that by controlling the vortex core energy, the antiferromagnetic Potts model can also exhibit the two topological phases, and, more interestingly, the two topological phases can overlap with each other.