When solid surfaces are immersed in aqueous solutions, some of their charges can dissociate, and in some experimental set-ups, they leave behind charged patches. When the surfaces are overall neutral, the nature of the surface charge distribution is crucial in determining the inter-surface interaction. Experiments have been conducted on such systems, where the surface charge was quenched and distributed in the form of patches. A long range attraction was observed, but it remains unexplained by van der Waals interactions between the two surfaces or by Debye-Hückel theory for ionic solutions.  In the present work, we calculate the osmotic pressure in such systems within the Poisson-Boltzmann framework. The osmotic pressure changes with the charge density and the inter-surface separation, but a new important quantity emerges – the charged-patch size. We show that even for relatively weakly charged and finite-size patches, the pressure profile as function of inter-plate separation has a complex behavior. In particular, we derive an expression for the crossover between repulsion and attraction.