  We investigate a generalized Aubry-Andr\'e-Harper (AAH) model with p-wave
superconducting pairing. Both the hopping amplitudes between the nearest
neighboring lattice sites and the on-site potentials in this system are
modulated by a cosine function with a periodicity of $1/\alpha$. In the
incommensurate case [$\alpha=(\sqrt{5}-1)/2$], due to the modulations on the
hopping amplitudes, the critical region of this quasiperiodic system is
significantly reduced and the system becomes more easily to be turned from
extended states to localized states. In the commensurate case ($\alpha = 1/2$),
we find that this model shows three different phases when we tune the system
parameters: Su-Schrieffer-Heeger (SSH)-like trivial, SSH-like topological, and
Kitaev-like topological phases. The phase diagrams and the topological quantum
numbers for these phases are presented in this work. This generalized AAH model
combined with superconducting pairing provides us with a useful testfield for
studying the phase transitions from extended states to Anderson localized
states and the transitions between different topological phases.
