value. To derive the modified Friedmann field equations (FFEs), we use entropies and the first law of thermodynamics. Thus, even in the presence of the typical interaction between the Ricci scalar and baryon current, this results in non-trivial modifications to the mass density and pressure content of the universe, which provides a viable mechanism allowing for baryogenesis. Finally, we show that even in the radiation-dominant era baryon asymmetry factor (BAF) is non-zero. We conclude, BE parameter 0 ≤ ∆ < 1, SME parameters R and δ with positive δ ≥ 4.2 × 1038 (keeping fixed R = 1) while at constant δ = 9 × 1028 for all values of R and for the generalized entropy parameter positive β ≤ 2.4 × 10−28 (fixing γ = α = 5); α ≤ 3.5 × 10−23 (for γ = 1.2 and β = 3) and γ ≥ 1.1 × 106 (at α = 3 × 10−20, β = 3), we have physically desired results on the observational ground.