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The recent discovery of the interfacial superconductivity (SC) of the Bi2Te3/Fe1+yTe heterostructure has attracted extensive studies due to its potential as a novel platform for trapping and controlling Majorana fermions. Here we present studies of another topological insulator (TI)/Fe1+yTe heterostructure, Sb2Te3/Fe1+yTe, which also has an interfacial 2-dimensional SC. The results of transport measurements support that reduction of the excess Fe concentration of the Fe1+yTe layer not only increases the fluctuation of its antiferromagnetic (AFM) order but also enhances the quality of the SC of this heterostructure system. On the other hand, the interfacial SC of this heterostructure was found to have a wider-ranging TI-layer thickness dependence than that of the Bi2Te3/Fe1+yTe heterostructure, which is believed to be attributed to the much higher bulk conductivity of Sb2Te3that enhances indirect coupling between its top and bottom topological surface states (TSSs). Our results provide evidence of the interplay among the AFM order, itinerant carries from the TSSs, and the induced interfacial SC of the TI/Fe1+yTe heterostructure system.