  In this paper, we present the most general non-relativistic Chern-Simons
gravity model in three spacetime dimensions. We first study the
non-relativistic limit of the Mielke-Baekler gravity through a contraction
process. The resulting non-relativistic theory contains a source for the
spatial component of the torsion and the curvature measured in terms of two
parameters, denoted by $p$ and $q$. We then extend our results by defining a
Newtonian version of the Mielke-Baekler gravity theory, based on a Newtonian
like algebra which is obtained from the non-relativistic limit of an enhanced
and enlarged relativistic algebra. Remarkably, in both cases, different known
non-relativistic and Newtonian gravity theories can be derived by fixing the
$\left(p,q\right)$ parameters. In particular, torsionless models are recovered
for $q=0$.
