under the Inönü-Wigner contracted (super)algebra by construction. Thus, the development of any CS action based on an Inönü-Wigner contracted (super)algebra is assured.[^2] In particular, the procedure presented in [@Concha:2016zdb] allows to obtain explicitly the CS supergravity action of a contracted superalgebra, which will be our case, since the $\mathcal{N}=1$ AdS Carroll superalgebra is obtained as a contraction of the $\mathcal{N}=1$ AdS superalgebra [@Bergshoeff:2015wma].

Having constructed the three-dimensional CS supergravity theory invariant under the AdS Carroll superalgebra, we subsequently apply the flat limit ($\ell \rightarrow \infty$, being $\ell$ the length parameter) at the level of the superalgebra, CS action, gauge transformation laws, and field equations. In particular, taking the flat limit of the AdS Carroll CS supergravity action we obtain the three-dimensional CS supergravity theory invariant under the super-Carroll algebra, which is a contraction of the Poincaré superalgebra (see [@Bergshoeff:2015wma]).

AdS Chern-Simons supergravity in 2+1 spacetime dimensions {#S1}
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It is well assumed that a three-dimensional (super)gravity theory can be described by a CS action as a gauge theory, offering an interesting toy model to approach higher-dimensional theories [@DK; @Deser; @PvN; @AT1; @RPvN; @Witten; @AT2; @NG; @Howe:1995zm; @Banados:1996hi; @Giacomini:2006dr]. In the last decades, diverse three-dimensional supergravity models have been studied, and 