  We study the properties and stability of nuclei in the inner crust of neutron
stars in the presence of strong magnetic fields $\sim 10^{17}$ G. Nuclei
coexist with a neutron gas and reside in a uniform gas of electrons in the
inner crust. This problem is investigated within the Thomas-Fermi model. We
extract the properties of nuclei based on the subtraction procedure of Bonche,
Levit and Vautherin. The phase space modification of electrons due to Landau
quantisation in the presence of strong magnetic fields leads to the enhancement
of electron as well as proton fractions at lower densities $\sim 0.001$
fm$^{-3}$. We find the equilibrium nucleus at each average baryon density by
minimising the free energy and show that, in the presence of strong magnetic
fields, it is lower than that in the field free case. The size of the spherical
cell that encloses a nucleus along with the neutron and electron gases becomes
smaller in strong magnetic fields compared with the zero field case. Nuclei
with larger mass and atomic numbers are obtained in the presence of strong
magnetic fields as compared with cases of zero field.
