  We investigate the vacuum expectation value of the fermionic current induced
by a magnetic flux in a (2+1)-dimensional conical spacetime in the presence of
a circular boundary. On the boundary the fermionic field obeys MIT bag boundary
condition. For irregular modes, a special case of boundary conditions at the
cone apex is considered, when the MIT bag boundary condition is imposed at a
finite radius, which is then taken to zero. We observe that the vacuum
expectation values for both charge density and azimuthal current are periodic
functions of the magnetic flux with the period equal to the flux quantum
whereas the expectation value of the radial component vanishes. For both
exterior and interior regions, the expectation values of the current are
decomposed into boundary-free and boundary-induced parts. For a massless field
the boundary-free part in the vacuum expectation value of the charge density
vanishes, whereas the presence of the boundary induces nonzero charge density.
Two integral representations are given for the boundary-free part in the case
of a massive fermionic field for arbitrary values of the opening angle of the
cone and magnetic flux. The behavior of the induced fermionic current is
investigated in various asymptotic regions of the parameters. At distances from
the boundary larger than the Compton wavelength of the fermion particle, the
vacuum expectation values decay exponentially with the decay rate depending on
the opening angle of the cone. We make a comparison with the results already
known from the literature for some particular cases.
