In this paper, we investigate the electrical transport properties of Zr-, La- and Pd-based metallic glassy fibers (MGFs) with diameters at microscale, which are fabricated by superplastic deformation at high temperatures. It is found that with the decrease of the diameter, the resistivity of the MGF increases with decreasing temperature more quickly. As compared to the thicker one, the structure of the thinner MGF is more strongly rejuvenated with a larger relaxation enthalpy, a larger average short-range atomic distance and less crystal-like structure induced by the larger normal stress during its formation process. Based on the evolution of the heterogeneous structure, the dependence of electrical resistivity on the size for the MGFs is interpreted within the extended Ziman liquid-metal theory. The results might be significant for controlling the electrical properties of MGFs via tunning their glassy states and applying them in micro-electromechanical systems.