The author develops a general formulation for the free energy of a hot Fermionic plasma confined in an arbitrary smooth potential barrier and a weak magnetic field. The well-known Wigner-Kirkwood expansion turns out to be powerful computational technique in the investigation. The explicit formulae obtained enable one to calculate exchange and confining effects on various physical properties of such systems. As an example, they are applied to calculations of exchange and confining corrections to the diamagnetic susceptibility and the specific heat. The author also constructs some examples by simple choices of the confining potential barrier.