  Motivated by a recent experiment on superfluid 3He-A confined in narrow
parallel plates using a rotating cryostat, we explore possible vortices stable
under magnetic field applied to arbitrary angle relative to the plates in order
to seek vortices which can accommodate the Majorana zero mode in the core.
After proving that the singular vortex with the unit winding number provides
the Majorana mode in the spinful situation, we establish the phase diagram in
the plane; the rotation frequency $\Omega$ vs system size R by finding possible
order parameter textures within the Ginzburg-Landau framework. We also analyze
the stability for a single and a pair of half-quantum vortices, which possesses
the Majorana mode in its core. It is concluded from the above mention that the
Majorana zero mode can be found in the present on-going experimental setting at
ISSP, Univ. Tokyo.
