  Majorana corner modes appearing in two-dimensional second-order topological
superconductors have great potential applications for fault-tolerant
topological quantum computations. We demonstrate that in the presence of an
in-plane magentic field two-dimensional ($s+p$)-wave superconductors host
Majorana corner modes, whose location can be manipulated by the direction of
the magnetic field. In addition, we discuss the effects of edge imperfections
on the Majorana corner modes. We describe how different edge shapes and edge
disorder affect the number and controllability of the Majorana corner modes,
which is of relevance for the implementation of topological quantum
computations. We also discuss tunneling spectroscopy in the presence of the
Majorana corner modes, where a lead-wire is attached to the corner of the
noncentrosymmetric superconductor. The zero-bias differential conductance shows
a distinct periodicity with respect to the direction of the magnetic field,
which demonstrates the excellent controllability of the Majorana corner modes
in this setup. Our results lay down the theoretical groundwork for observing
and tuning Majoran corner modes in experiments on ($s+p$)-wave superconductors.
