This study introduces a mathematical model that describes the Magnetohydrodynamics (MHD) flow of blood in a porous stenosis artery, incorporating a new hybrid nanofluid (HNF) model known as ‘Quadruple’ or the tetra-(HNF) model. An innovative aspect of this study lies in the unexplored combination of tetra-hybrid nanoparticles with the Sisko rheological model. The conventional Tiwari and Das (HNF) model has been expanded to accommodate the tetra-(HNFs) case. To transform the governing partial differential equations into ordinary differential equations, a series of variable similarity transformations are employed. The resulting highly nonlinear simultaneous equations are efficiently solved using the shooting method. Numerical computations are conducted to investigate various parametric conditions, and graphs are utilized to visualize notable aspects of flow velocity and temperature. A comprehensive analysis is provided to illustrate the influence of flow parameters on wall shear stress and local Nusselt number, which are depicted through figures and tables. The study shows that the novel tetra-HNF exhibits enhancements in blood flow when compared to nanofluids with a lower number of hybrids. Increasing the flow power index of non-Newtonian Sisko model leads to improve convective heat transfer. Furthermore, parameters such as porosity, thermal radiation, and magnetic effects exhibit noticeable impacts on blood flow, temperature, and associated risks in constricted arteries.