Irrespective of whether Active Galactic Nuclei (AGN) is cored with Supermassive Black Holes (SMBH) or not, there is a general consensus that observations indicate that the AGN plays fundamental role in galaxy evolution. The accretion disc powered fueling of the AGN and counter-feedback on its environment in the form of stress-energy-momentum along the radial component and an associated polodial jets seems viable model. On the theoretical ground there is no unified theory that compromise the observations. But there are pull of such diverse physics simulated to describe the observational works. So, there is unsettled theoretical framework how the activity of the AGN plays role in the evolution of host galaxy. Motivated by this we studied the role of AGN on its host galaxy evolution where General relativistic (GR) Magnetohydrodynamics (MHD) equation is considered to derive radial pressure that invokes star forming cold gases. Methodologically the central engine of the AGN is considered with SMBH/pseudo-SMBH. Locally, around the AGN, Reissner-Nordstrom-de Sitter metric is considered that reduces to the Schwarzschoild-de Sitter (SdS) background. Geometrically, a simple spherical geometry is superimposed with central disc structure assumed by cored void mass ablating model. The results of the work indicates that the AGN plays role in galaxy evolution, especially in the nearby environment. Also we report that the adjacent envelope to the AGN seems quiet with no activity in formation.