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The magnetic, transport, and magnetotransport properties of Mn3+xSn1-xC (0 <= x <= 0.4) and Mn3ZnySn1-yC (0 <= y <= 0.9) compounds are investigated systematically. For Mn3+xSn1-xC, a sharp rise in temperature dependence of resistivity is observed for x <= 0.1, accompanied by a magnetic phase transition from a paramagnetic state to a complicated spin arrangement composed of antiferromagnetic and ferromagnetic sublattices. A different behavior appears in the resistivity of Mn3.2Sn0.8C, which decreases monotonically with decreasing temperature. A partial Zn substitution for Sn in Mn3SnC leads to dramatic changes of magnetic and transport properties. As the temperature decreases, a magnetic transition from the ferromagnetic (or ferrimagnetic) to antiferromagnetic state occurs at about 170 and 142 K for Mn3Zn0.4Sn0.6C and Mn3Zn0.5Sn0.5C compounds, respectively, which strongly affects their transport properties. A significant magnetoresistance as large as 34% is observed for Mn3Zn0.5Sn0.5C at 95 K, in accordance with a field-induced metamagnetic transition. The origin of the magnetoresistance effect is discussed in terms of the reconstruction of the Fermi surface.