This research explores the dynamic behavior of magnetohydrodynamic (MHD) flow and radiative heat transfer in a Casson Ternary Nanofluid (TN) as it flows between two parallel plates. Thermal and mass transmission characteristics of this type of flow, particularly in the existence of magnetic fields, have not been explored. There are various industrial applications of squeezing flow such as the movement between pistons and nozzles in vehicle engines, hence the study of squeezing flow is important. The TN is composed of three types of nanoparticles, graphene, graphene oxide and silver with sodium alginate based. By applying similarity variables, the governing equations are converted to dimensionless forms and solved using the Keller-box method. The results are compared with existing data, showing satisfactory alignment, thus validating the method. The research focuses on the effects of squeezing, magnetic fields, nanoparticle volume fractions, viscous dissipation and thermal radiation on flow characteristics and physical properties. The findings reveal that squeezing the parallel plates increases fluid velocity, with a deceleration in the center as parameters like Ha, ϕ1, ϕ2 and ϕ3 increase. Furthermore, both convective heat transfer and temperature decrease with higher values of ϕ1, ϕ2 and ϕ3. Hence, TN are concluded more efficient aimed at applications of heat transmission.