  Off-diagonal Aubry-Andr\'{e} (AA) model has recently attracted a great deal
of attention as they provide condensed matter realization of topological
phases. We numerically study a generalized off-diagonal AA model with p-wave
superfluid pairing in the presence of both commensurate and incommensurate
hopping modulations. The phase diagram as functions of the modulation strength
of incommensurate hopping and the strength of the p-wave pairing is obtained by
using the multifractal analysis. We show that with the appearance of the p-wave
pairing, the system exhibits mobility-edge phases and critical phases with
various number of topologically protected zero-energy modes. Predicted
topological nature of these exotic phases can be realized in a cold atomic
system of incommensurate bichromatic optical lattice with induced p-wave
superfluid pairing by using a Raman laser in proximity to a molecular
Bose-Einstein condensation.
