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Using the quantum magnetohydrodynamics model, linear dispersion of magnetosonic waves are studied in a quasineutral quantum electron-ion plasmas in two distinct regimes of nonrelativistic and relativistic degeneracies taking into account the plasma composition effect. It is shown that the paramagnetic spin effects of the degenerated electrons plays a key role in dynamics of magnetosonic waves. The linear wave speed is found to have minimum value at some degeneracy parameter value in such plasmas. This is due to delicate interplay between relativistic degeneracy and the Pauli spin magnetization. It is also revealed that the plasma composition has significant effect on the linear dispersion of the relativistic degeneracy limit contrary to that of nonrelativistic case, and Zeeman energy has significant effect in nonrelativistic degeneracy regime unlike that of relativistic one in the linear perturbation limit. Current findings can have important applications in both inertial plasma confinement and astrophysical degenerate plasmas.