This innovative study investigates the flow of ternary hybrid nanofluid containing gyrotactic microorganisms in microchannel. The magnetic field, thermophoresis, and Brownian motion effects are analyzed. The transformation of the PDEs system into ODEs is carried out by using the group transformation method. The innovative findings examine the Newtonian and non-Newtonian models derived from the system of ODEs. Several graphs illustrate how different parameters affect the velocity profile, temperature, concentration, and microorganisms. The power-law index value increases the fluid flow velocity by about 9% at n = 3, 36% at n = 4 relative to the case of n = 2.5 at the center of the boundary layer. Moreover, the ternary hybrid nanofluid exhibits a greater temperature compared to the nanofluid. The current results are compared to the researchers' findings to confirm the validity of the obtained results. When the Prandtl number is between 6 and 10, the Nusselt number reaches 45.49%.