A non-traditional approach to the computer simulation study of a class of quasi-two-dimensional Coulomb systems (charged particles confined to a layer near a charged planar surface) is presented. The essence of the approach lies in exploiting the fact that the charged confinement is of finite dimensions. The main consequence of such a finiteness is a non-zero potential gradient along the finite charged area that includes a non-zero tangential component of the electric field. A system of like-charged spherical particles confined by the planar surface that includes an oppositely charged squared area is considered as an example. We find that the like-charged particles, independent of their concentration, all become confined on the oppositely charged area, if the surface charge balances the total charge carried by the particles, and if the electrostatic coupling is sufficiently large. The local density of the particles above the charged area is not homogeneous; near the boundaries of the charged square a clear tendency of layer formation along the square sides is observed.