  The quantum-mechanical problem of constructing a self-adjoint Hamiltonian for
the Dirac equation in an Aharonov--Bohm field in 2+1 dimensions is solved with
taking into account the fermion spin. The one-parameter family of self-adjoint
extensions is found for the above Dirac Hamiltonian with particle spin. The
correct domain of the self-adjoint Hamiltonian extension selecting by means of
acceptable boundary conditions can contain regular and singular (at the point
${\bf r}=0$) square-integrable functions on the half-line with measure $rdr$.
We argue that the physical reason of the existence of singular solutions is the
additional attractive potential, which appear due to the interaction between
the spin magnetic moment of fermion and Aharonov--Bohm magnetic field. For some
range of parameters there are bound fermionic states. It is shown that fermion
(particle and antiparticle) states with zero energy are intersected what
signals on the instability of quantum system and the possibility of a
fermion-antifermion pair creation by the static external field.
