  We describe the self-adjoint realizations of the operator $H:=-i\alpha\cdot
\nabla + m\beta + \mathbb V(x)$, for $m\in\mathbb R $, and $\mathbb V(x)=
|x|^{-1} ( \nu \mathbb{I}_4 +\mu \beta -i \lambda
\alpha\cdot{x}/{|x|}\,\beta)$, for $\nu,\mu,\lambda \in \mathbb R$. We
characterize the self-adjointness in terms of the behaviour of the functions of
the domain in the origin, exploiting Hardy-type estimates and trace lemmas.
Finally, we describe the distinguished extension.
