  We study the spectral and wavefunction properties of a one-dimensional
incommensurate system with p-wave pairing and unveil that the system
demonstrates a series of particular properties in its ciritical region. By
studying the spectral statistics, we show that the bandwidth distribution and
level spacing distribution in the critical region follow inverse power laws,
which however break down in the extended and localized regions. By performing a
finite-size scaling analysis, we can obtain some critical exponents of the
system and find these exponents fulfilling a hyperscaling law in the whole
critical region. We also carry out a multifractal analysis on system's
wavefuntions by using a box-counting method and unveil the wavefuntions
displaying different behaviors in the critical, extended and localized regions.
