  We calculate the $\delta f$ correction to the one particle distribution
function in presence of magnetic field and non-zero shear viscosity within the
relaxation time approximation. The $\delta f$ correction is found to be
electric charge dependent. Subsequently, we also calculate one longitudinal and
four transverse shear viscous coefficients as a function of dimensionless Hall
parameter $\chi_{H}$ in presence of the magnetic field. We find that a proper
linear combination of the shear viscous coefficients calculated in this work
scales with the result obtained from Grad's moment method in
\cite{Denicol:2018rbw}. Calculation of invariant yield of $\pi^{-}$ in a simple
Bjorken expansion with cylindrical symmetry shows no noticeable change in
spectra due to the $\delta f$ correction for realistic values of the magnetic
field and relaxation time. However, when transverse expansion is taken into
account using a blast wave type flow field we found noticeable change in
spectra and elliptic flow coefficients due to the $\delta f$ correction. The
$\delta f$ is also found to be very sensitive on the magnitude of magnetic
field. Hence we think it is important to take into account the $\delta f$
correction in more realistic numerical magnetohydrodynamics simulations.
