In this study, we unravel the intricate dynamics of a spatio-temporal prey-predator model featuring a Holling type-IV functional response and Leslie-type predator numerical response under Neumann boundary conditions. Our analysis encompasses the uniform persistence and global asymptotic stability of a positive equilibrium, validated by precise numerical simulations. Additionally, we explore Turing instability and spatial pattern emergence through linear stability analysis. Our primary emphasis lies in the realm of spatio-temporal bifurcation analysis, through which we establish criteria for the presence or absence of non-constant steady states within n-dimensional diffusion models. Moreover, we discern precise conditions governing Hopf bifurcation and steady-state bifurcation in 1-dimensional diffusion models. These findings offer theoretical insights that align with the intricate dynamic patterns observed in our numerical simulations.