  Despite the experimental success of general relativity in the scales it has
been tested, there are still some inconsistencies, such as explaining the
acceleration of the universe and singularities. $f(R)$ gravity has emerged to
provide corrections to the Ricci scalar, leading to new equations of motion
that could explain this acceleration. On the other hand, Regular Black Holes,
supported by non-linear electrodynamics, have well-defined curvature scalars
but often violate energy conditions. In this work, we investigate how to obtain
regular solutions in $(2+1)$ dimensions by considering $f(R)$ gravity and
non-linear electrodynamics. Subsequently, we find that non-linear
electrodynamics models that guarantee regular solutions in General Relativity
do not produce regular solutions in $f(R)$ theory. Finally, we observe that
energy conditions are still violated in $f(R)$ gravity.
