  The superconducting state typically favors a uniform spatial distribution
akin to ferromagnetism. Nevertheless, the pair-density-wave state exhibits sign
changes in the pairing order, leading to potential frustrations in phase
coherence.We propose a mechanism to the sextetting order stemming from the
frustrations in the phase coherence of a pair-density-wave state, whose spatial
modulation manifests a vortex-antivortex honeycomb lattice. The classical
ground state configurations are mapped to Baxter's three-coloring model,
revealing a macroscopic degeneracy accompanied by extensive entropy. The phase
coherence problem intertwines the U(1) phases and the vorticity variables.
While the resultant color and phase fluctuations suppress the pair-density-wave
order, they maintain the sextetting order above the superconducting transition
temperature ($T_{\text{c}}$). The $1/3$-fractional vortex emerges as the
fundamental topological defect in the sextetting order. This novel mechanism of
frustrated superconductivity provides an alternative explanation for the
experimental observed fractional oscillations in CsV$_3$Sb$_5$.
