This paper considers the Schrödinger–Newton (SN) equation with a Yukawa potential, introducing the effect of locality. We also include the interaction of the self-gravitating quantum matter with a radiation background, describing the effects due to the environment. Matter and radiation are coupled by photon scattering processes and radiation pressure. We apply this extended SN model to the study of Jeans instability and gravitational collapse. We show that the instability thresholds and growth rates are modified by the presence of an environment. The Yukawa scale length is more relevant for large-scale density perturbations, while the quantum effects become more relevant at small scales. Furthermore, coupling with the radiation environment modifies the character of the instability and leads to the appearance of two distinct instability regimes: one, where both matter and radiation collapse together, and others where regions of larger radiation intensity coincide with regions of lower matter density. This could explain the formation of radiation bubbles and voids of matter. The present work extends the SN model in new directions and could be relevant to astrophysical and cosmological phenomena, as well as to laboratory experiments simulating quantum gravity.