  A relativistic version of cold emission of electrons in presence of strong
magnetic field, relevant for strongly magnetized neutron stars is obtained. It
is found that in this scenario, a scalar type potential barrier does not allow
quantum tunneling through the surface. Whereas, in presence of a vector type
surface barrier, the probability of electron emission is much larger compared
to the original Fowler-Nordheim cold emission of electrons. It is found that
the relativistic version in presence of strong magnetic field does not follow
exponential decay.
