  Quantum criticality nearby a certain magnetic phase transition beneath the
superconducting dome of $\mathrm{Ba_{1-x}Na_xFe_2As_2}$ is attentively studied
by virtue of a phenomenological theory in conjunction with renormalization
group approach. We report that ordering competition between magnetic and
superconducting fluctuations is capable of coaxing incommensurate (IC) magnetic
states to experience distinct fates depending upon their spin configurations.
The $C_2$-symmetry IC magnetic stripe with perpendicular magnetic helix
dominates over other $C_2$-symmetry magnetic competitors and hints at a
potential candidate for the unknown $C_2$-symmetry magnetic state. Amongst
$C_4$-symmetry IC magnetic phases, IC charge spin density wave is substantiated
to be superior, shedding light on the significant intertwining of charge and
spin degrees of freedom. Meanwhile, ferocious fluctuations render a sharp fall
of superfluid density alongside dip of critical temperature as well as
intriguing behavior of London penetration depth.
