  We study fermions in a magnetic field in a finite size cylinder. With the
boundary condition for the fermion flux, we show that the energy spectra and
the wave-functions are modified by the finite size effect; the boundary makes
the degenerate Landau levels appear only partially for states with small
angular momenta, while the boundary effect becomes stronger for states with
large angular momenta. We find that mode accumulation at the boundary occurs
for large angular momenta and the magnetic effect is enhanced on the boundary
surface. Using a simple fermionic model, we quantify the magnetic catalysis,
i.e. the magnetic enhancement of the fermion pair condensation, in a finite
size cylinder. We confirm that the magnetic catalysis is strongly amplified at
the boundary due to the mode accumulation.
