At present, there is no cosmological model that accurately explains and predicts the distribution of clustered dark matter in typical galaxies. The attempts to reconcile the observations and simulations lead to different density profiles of the astrophysical clustered dark matter distribution of typical galaxy.  In a different approach, we attempt to focus on a cosmological model having the small deviation from the Einstein's gravity theory and predict the density profile via the combined astrophysical observations of lensing angle and rotation velocity profiles of typical galaxy in the modified gravity framework.