  Using Monte Carlo simulations and finite-size scaling, we study three-state
Potts antiferromagnet on layered square lattice with two and four layers
$L_z=2$ and $4$. As temperature decreases, the system develops quasi-long-range
order via a Berezinskii-Kosterlitz-Thouless transition at finite temperature
$T_{c1}$. For $L_z=4$, as temperature is further lowered, a long-range order
breaking the $Z_6$ symmetry develops at a second transition at $T_{c2} <
T_{c1}$. The transition at $T_{c2}$ is also
Berezinskii-Kosterlitz-Thouless-like, but has magnetic critical exponent
$\eta=1/9$ instead of the conventional value $\eta = 1/4$. The emergent $U(1)$
symmetry is clearly demonstrated in the quasi-long-range ordered region $T_{c2}
\leq T \leq T_{c1}$.
