  Exact analytic solutions are found for the Dirac equation in 2+1 dimensions
for a spin-one-half particle in a combination of the Lorentz 3-vector and
scalar Coulomb as well as Aharonov--Bohm potentials. We employ the
two-component Dirac equation which contains a new parameter introduced by Hagen
to describe the spin of the spin-1/2 particle. We derive a transcendental
equations that implicitly determine the energy spectrum of an electron near the
negative-energy continuum boundary and the critical charges for some electron
states. Fermion pair production from a vacuum by a strong Coulomb field in the
presence of the magnetic flux tube of zero radius is considered. It is shown
that the presence of the Ahanorov--Bohm flux tends to stabilize the system.
