  In this paper, we determine the bound-state solutions for Dirac fermions with
electric dipole moment (EDM) and position-dependent mass (PDM) in the presence
of a radial magnetic field generated by magnetic monopoles. To achieve this, we
work with the (2+1)-dimensional (DE) Dirac equation with nonminimal coupling in
polar coordinates. Posteriorly, we obtain a second-order differential equation
via quadratic DE (simplified by a similarity transformation). Solving this
differential equation through a change of variable and the asymptotic behavior,
we obtain a generalized Laguerre equation. From this, we obtain the bound-state
solutions of the system, given by the two-component Dirac spinor and by the
relativistic energy spectrum. So, we note that such spinor is written in terms
of the generalized Laguerre polynomials, and such spectrum (for a fermion and
an antifermion) is quantized in terms of the radial and total magnetic quantum
numbers $n$ and $m_j$, and explicitly depends on the EDM $d$, PDM parameter
$\kappa$, magnetic charge density $\lambda_m$, and on the spinorial parameter
$s$. In particular, the quantization is a direct result of the existence of
$\kappa$ (i.e., $\kappa$ acts as a kind of ``external field or potential'').
Besides, we discuss in detail the characteristics of the spectrum as well as
graphically analyze the behavior of the spectrum as a function of $\kappa$ and
$\lambda_m$ for three different values of $n$ (ground state and the first two
excited states).
