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The effect of different atomic substitutions at Mn sites on the magnetic and magnetocaloric properties in Ni50Mn35Co2Sn13 alloy has been studied in detail. The substitution of Ni or Co for Mn atoms might lower the Mn content at Sn sites, which would reduce the d-d hybridization between Ni 3d eg states and the 3d states of excess Mn atoms at Sn sites, thus leading to the decrease of martensitic transformation temperature TM in Ni51Mn34Co2Sn13 and Ni50Mn34Co3Sn13 alloys. On the other hand, the substitution of Sn for Mn atoms in Ni50Mn34Co2Sn14 would enhance the p-d covalent hybridization between the main group element (Sn) and the transition metal element (Mn or Ni) due to the increase of Sn content, thus also reducing the TM by stabilizing the parent phase. Due to the reduction of TM, a magnetostructural martensitic transition from FM austenite to weak-magnetic martensite is realized in Ni51Mn34Co2Sn13 and Ni50Mn34Co2Sn14, resulting in a large magnetocaloric effect around room temperature. For a low field change of 3 T, the maximum ∆SM reaches as high as 30.9 J/kg K for Ni50Mn34Co2Sn14. A linear dependence of ΔSM upon μ0H has been found in Ni50Mn34Co2Sn14, and the origin of this linear relationship has been discussed by numerical analysis of Maxwell’s relation.