By incorporating leading c -dependent corrections to the Carroll transformations, we introduce the post-Carroll transformations". We demonstrate that these transformations are consistent with post-Carrollian mechanics [1]; furthermore, they give rise to the so-called post-Carroll algebra". We show that, unlike the Carroll algebra, this new structure allows for a central charge in higher dimensions; we refer to it as the Carroll{Bargmann algebra". To construct conformal extensions, we first build the conformal extension of the post-Carroll algebra and study field theories invariantunder this symmetry. We then construct the conformal extension of the Carroll{Bargmann algebra, referred to as the Carroll{Schrodinger algebra", and demonstrate that it precisely matches the symmetry algebra of the higher-dimensional Carroll{Schrodinger theory [2]. Finally, we derive the general form of two-point functions in a post-Carrollian CFT, which in 1 + 1 dimensions exhibits both electric and magnetic sectors, while in higher dimensions only the magnetic sector survives.