  In this work, we study the spin texture of a class of higher-order
topological superconductors (HOTSC) and show how it can be used to detect and
braid Majorana corner modes (MCMs). This class of HOTSC is composed of
two-dimensional topological insulators with s-wave superconductivity and
in-plane magnetic fields, which offers advantages in experimental
implementation. The spin polarization of the MCMs in this class is
perpendicular with the applied magnetic field direction and is opposite on
intrinsic orbitals, resulting in an overall ferrimagnetic spin texture. As a
result, we find that the spin-selective Andreev reflection can be observed in a
transverse instead of parallel direction to the applied magnetic field.
Meanwhile, this spin texture leads to the gate-tunable $4\pi$ periodic $\phi_0$
Josephson current that performs qualitatively different behavior from the
topologically trivial $\phi_0$-junction under rotating the in-plane magnetic
field. Meanwhile, the existence of the MCMs in this class does not depend on
the in-plane magnetic field direction. This gives rise to great advantage in
constructing all electronically controlled Majorana network for braiding, which
is confirmed through our numerical simulation. We thus provide a comprehensive
scheme for probing non-Abelian statistics in this class of HOTSCs.
