  This paper investigates a new class of regular black hole solutions in (2 +
1)-dimensions by introducing a generalization of the quasi-localized matter
model proposed by Estrada and Tello-Ortiz. Initially, we try to physically
interpret the matter source encoded in the energy-momentum tensor as
originating from nonlinear electrodynamics. We show, however, that the required
conditions for the quasi-locality of the energy density are incompatible with
the expected behavior of nonlinear electrodynamics, which must tend to
Maxwell's theory on the asymptotic limit. Despite this, we propose a
generalization for the quasi-localized energy density that encompasses the
existing models in the literature and allows us to obtain a class of regular
black hole solutions exhibiting remarkable features on the event horizons and
their thermodynamic properties. Furthermore, since the usual version of the
first law of thermodynamics, due to the presence of the matter fields, leads to
incorrect values of entropy and thermodynamics volume for regular black holes,
we propose a new version of the first law for regular black holes.
