  In this paper, by means of regularisation procedure via $r\to
\sqrt{r^2+l_0^2}$ (where $l_0$ can play the role of zero point length), we
first modify the gravitational and electromagnetic potentials in two dimensions
and then we solve the Einstein field equations to end up with an exact and
regular black hole solution in three dimensions with a negative cosmological
constant. We show that, the black hole solution is asymptotically AdS,
non-singular at the origin and, under specific conditions, it has a flat de
Sitter core at the origin. As a special case, we obtain the charged
Banados-Teitelboim-Zanelli (BTZ) solution. Finally, using a dimensional
continuation and the NJ algorithm, we end up with a legitimate rotating black
hole solution in three dimensions.
