  We systematically investigate the topological and localization properties of
a quadrupolar insulator represented by the celebrated
Benalcazar-Bernevig-Hughes model in presence of a quasiperiodic disorder
instilled in its hopping amplitude. While disorder can be detrimental to the
existence of the topological order in a system, we observe the emergence of a
disorder driven topological phase where the original (clean) system
demonstrates trivial behavior. This phenomenon is confirmed by the re-emergence
of zero energy states in the bandstructure together with a non-zero bulk
quadrupole moment, which in turn establishes the bulk boundary correspondence
(BBC). Furthermore, the distribution of the excess electronic charge shows a
pattern that is reminiscent of the bulk quadrupole topology. To delve into the
localization properties of the mid-band states, we compute the inverse
participation and normalized participation ratios. It is observed that the
in-gap states become critical (multifractal) at the point that discerns a
transition from a topological localized to a trivial localized phase. Finally,
we carry out a similar investigation to ascertain the effect of the
quasiperiodic disorder on the quadrupolar insulator when the model exhibits
topological properties in the absence of disorder. Again, we note a
multifractal behavior of the eigenstates in the vicinity of the transition.
