  Even though the crystallize nature of the neutron star crust plays a pivotal
role in describing various fascinating astrophysical observations, its
microscopic structure is not fully understood in the presence of a colossal
magnetic field. In the present work, we study the crustal properties of a
neutron star within an effective relativistic mean field framework in the
presence of magnetic field strength $\sim 10^{17}$G. We calculate the
equilibrium composition of the outer crust by minimizing the Gibbs free energy
using the most recent atomic mass evaluations. The magnetic field significantly
affects the equation of state (EoS) and the properties of the outer crust, such
as neutron drip density, pressure, and melting temperature. For the inner
crust, we use the compressible liquid drop model for the first time to study
the crustal properties in a magnetic environment. The inner crust properties,
such as mass and charge number distribution, isospin asymmetry, cluster
density, etc., show typical quantum oscillations (De Haas-van Alphen effect)
sensitive to the magnetic field's strength. The density-dependent symmetry
energy influences the magnetic inner crust like the field-free case. We study
the probable modifications in the pasta structures and it is observed that
their mass and thickness changes by $\sim 10-15 \%$ depending upon the magnetic
field strength. The fundamental torsional oscillation mode frequency is
investigated for the magnetized crust in the context of quasiperiodic
oscillations (QPO) in soft gamma repeaters. The magnetic field strengths
considered in this work influences only the EoS of outer and shallow regions of
the inner crust, which results in no significant change in global neutron star
properties. However, the outer crust mass and its moment of inertia increase
considerably with increase in magnetic field strength.
