  The focus of this paper is the study of the inverse point-source scattering
problem, specifically in relation to a certain class of electric potentials.
Our research provides a novel uniqueness result for the inverse problem with
local data, obtained from the near field pattern. Our work improves the work of
Caro and Garcia, who investigated both the direct problem and the inverse
problem with global near field data for critically singular and $\delta$-shell
potentials. The primary contribution of our research is the introduction of a
Runge approximation result for the near field data on the scattering problem
which, in combination with an interior regularity argument, enables us to
establish a uniqueness result for the inverse problem with local data.
Additionaly, we manage to consider a slightly wider class of potentials.
