The two-fluid magnetohydrodynamic theory is applied to study periodic magnetosonic waves (cnoidal waves) in electron-ion ( \(e-i\) ) classically magnetized plasma. The mass of electrons is included in the momentum equation to incorporate the inertial effects, and they obey nonthermal distributions such as (r, q), Q-nonextensive, and kappa distributions via the equation of state. The dispersion relation (DR) for a magnetosonic wave (MWs) is derived by applying the Fourier transformation. The dispersion in the plasma system appears through electron skin depth. By employing the Reductive Perturbation Technique (RPT), a nonlinear evolution equation is formulated, which allows for the existence of solitons within the plasma system. To obtain the solution in the form of magnetosonic cnoidal waves, the Sagdeev pseudopotential method is utilized. The research comprehensively examines how changes in the electron flatness index (r) at low energy, the superthermal index (q) at high energy, the superthermal parameter ( \(\kappa \) ), and the nonextensive parameter (Q) affect the propagation properties of magnetosonic waves. The findings reveal that when \(\vartheta =\Lambda =0\) , the cnoidal waves associated with magnetosonic waves undergo a transformation and become solitary waves. Overall, the findings enhance the understanding of ion-acoustic periodic magnetosonic waves in ionospheric plasmas and single-mode drift wave spectra.
