  In this paper, we present novel non-relativistic superalgebras which
correspond to supersymmetric extensions of the enlarged extended Bargmann
algebra. The three-dimensional non-relativistic Chern-Simons supergravity
actions invariant under the aforementioned superalgebras are constructed. The
new non-relativistic superalgebras allow to accommodate a cosmological constant
in a non-relativistic supergravity theory. Interestingly, we show that one of
the non-relativistic supergravity theories presented here leads to the recently
introduced Maxwellian exotic Bargmann supergravity when the flat limit $\ell
\rightarrow\infty$ is considered. Besides, we show that both descriptions can
be written in terms of a supersymmetric extension of the Nappi-Witten algebra
or the extended Newton-Hooke superalgebra.
