  We present 850 $\mu$m polarization and $\rm C^{18}O (3-2)$ molecular line
observations toward the X-shaped nebula in the California molecular cloud using
the JCMT SCUBA-2/POL-2 and HARP instruments. The 850 $\mu$m emission shows that
the observed region includes two elongated filamentary structures (Fil1 and
Fil2) having chains of regularly spaced cores. We measured the mass per unit
length of the filament and found that Fil1 and Fil2 are thermally super- and
subcritical, respectively, but both are subcritical if nonthermal turbulence is
considered. The mean projected spacings ($\Delta\bar S$) of cores in Fil1 and
Fil2 are 0.13 and 0.16 pc, respectively. $\Delta\bar S$ are smaller than
$4\times$filament width expected in the classical cylinder fragmentation model.
The large-scale magnetic field orientations shown by Planck are perpendicular
to the long axes of Fil1 and Fil2, while those in the filaments obtained from
the high-resolution polarization data of JCMT are disturbed, but those in Fil1
tend to have longitudinal orientations. Using the modified
Davis-Chandrasekhar-Fermi (DCF) method, we estimated the magnetic field
strengths ($B_{\rm pos}$) of filaments which are 110$\pm$80 and 90$\pm$60
$\mu$G. We calculated the gravitational, kinematic, and magnetic energies of
the filaments, and found that the fraction of magnetic energy is larger than 60
% in both filaments. We propose that a dominant magnetic energy may lead the
filament to be fragmented into aligned cores as suggested by Tang et al., and a
shorter core spacing can be due to a projection effect via the inclined
geometry of filaments or due to a non-negligible, longitudinal magnetic fields
in case of Fil1.
