This effort investigates the arrival of magnetothermal convection of ethylene glycol‐silver Jeffrey nanofluid in a Hele‐Shaw cell utilizing the linear stability concept. The model practiced for the Jeffrey nanofluid includes the impacts of Brownian movement and thermophoresis. The norms for both marginal and overstable modes of convections are developed analytically. The impact of magnetic Chandrasekhar number QM, magnetic Prandtl number Prm, Jeffrey parameter δ, Hele‐Shaw number HS, and a variety of nanofluid parameters such as the volumetric fraction of nanoparticles ϕ, nanoparticle Rayleigh number Rp, adjusted diffusive ratio NA, and Lewis number italicLe on the beginning of convective motion are investigated, and results are illustrated graphically. It is observed that the overstable approach of convection is probable below the certain threshold estimate of the magnetic Prandtl number Prm. This threshold estimate of the magnetic Prandtl number Prm upturns with a rise in the rate of QM, HS, and δ, while it drops with a surge in the nanofluid parameters. The system was found to be more stable by decreasing the Hele‐Shaw number HS, the Jeffery parameter δ, and nanofluid parameters, while it was unstable by decreasing the magnetic Chandrasekhar number QM and the magnetic Prandtl number Prm.