Flow past square and rectangular cylinder is an exciting fluid mechanics problem. The rectangular cylinder has been investigated both experimentally and numerically by various researchers due to the enormous practical significance. These include flow past tall buildings, cooling towers and chimneys associated with power plants, fuel storage tanks, off-shore structures, electronic chips etc. The interesting flow fields downstream of the cylinder and the flow field's modification to control fluid flow have gained recent researcher's interest. The present study focuses on the effect of suction/blowing boundary conditions on the fluid flow and heat transfer past rectangular cylinder with fillet in the low Reynolds number regime. The application of suction and blowing on different faces of the cylinder has been proved as an effective flow control method. For that, the governing equations of fluid flow and heat transfer are solved in the Cartesian framework using an in-house code based on Streamline upwind/Petrov-Galerkin (SUPG finite element method). The effect of suction and blowing boundary conditions applied at the fillet is studied for different aspect ratios and Reynolds number. Temperature and flow field characteristics have been presented and discussed with temperature contours and vorticity plots. The objective behind the present study is to find ways of reducing drag and to enhance the heat transfer past rectangular cylinder with fillets. By modifying the rectangular cylinder with fillets on the corner and applying the boundary conditions the flow fields gets modified in a manner so as to aid drag reduction and enhanced heat transfer.