EN
Electronic surface states localized on the edge of a semi-infinite square lattice are studied in the tight binding approximation. We examined the existence of surface states in the presence of magnetic field applied in the surface region of a 2D lattice. The applied field is perpendicular to the lattice and confined to a stripe near the surface. We also included a surface site perturbation caused by the presence of the surface. The magnetic field is introduced into the model by the Peierls substitution.