  We investigate a generalized interpolating Aubry-Andr\'{e}-Fibonacci (IAAF)
model with p-wave superconducting pairing. In the Aubry-Andr\'{e} limit, we
demonstrate that the system experiences transitions from a pure phase, either
extended or critical, to a variety of intermediate phases and ultimately enters
a localized phase with increasing potential strength. These intermediate phases
include those with coexisting extended and localized states, extended and
critical states, localized and critical states and a mix of extended, critical
and localized states. Each intermediate phase exhibits at least one type of
mobility edge separating different states. As the system approaches the
Fibonacci limit, both the extended and localized phases diminish, and the
system tends towards a critical phase.
