  The effect of edge on wetting and layering transitions of a three-dimensional
spin-1/2 Ising model is investigated, in the presence of longitudinal and
surface magnetic fields, using mean field (MF) theory and Monte Carlo (MC)
simulations. For T=0, the ground state phase diagram shows that there exist
only three allowed transitions, namely: surface and bulk transition, surface
transition and bulk transition. However, there exist a surface intra-layering
temperature $T_{L}^{s}$, above which the surface and the intra-layering surface
transitions occur. While the bulk layering and intra-layering transitions
appear above an other finite temperature $T_{L}^{b} (\ge T_{L}^{s})$. These
surface and bulk intra-layering transitions are not seen in the perfect
surfaces case.
  Numerical values of $T_{L}^{s}$ and $T_{L}^{b}$, computed by Monte Carlo
method are found to be smaller than those obtained using mean field theory.
However, the results predicted by the two methods become similar, and are
exactly those given by the ground state phase diagram, for very low
temperatures. On the other hand, the behavior of the local magnetizations as a
function of the external magnetic field, shows that the transitions are of the
first order type. $T_{L}^{s}$ and $T_{L}^{b}$ decrease when increasing the
system size and/or the surface magnetic field. In particular, $T_{L}^{b}$
reaches the wetting temperature $T_{w}$ for sufficiently large system sizes.
