  We investigate the interplay between disorder and superconducting pairing for
a one-dimensional $p$-wave superconductor subject to slowly varying
incommensurate potentials with mobility edges. With amplitude increments of the
incommensurate potentials, the system can undergo a transition from a
topological phase to a topologically trivial localized phase. Interestingly, we
find that there are four mobility edges in the spectrum when the strength of
the incommensurate potential is below a critical threshold, and a novel
topologically nontrivial localized phase emerges in a certain region. We reveal
this energy-dependent metal-insulator transition by applying several numerical
diagnostic techniques, including the inverse participation ratio, the density
of states and the Lyapunov exponent. Nowadays, precise control of the
background potential and the $p$-wave superfluid can be realized in the
ultracold atomic systems, we believe that these novel mobility edges can be
observed experimentally.
