The iron-chalcogenide high temperature superconductor Fe(Se,Te) (FST) has been reported to exhibit complex magnetic ordering and nontrivial band topology which may lead to novel superconducting phenomena. However, the recent studies have so far been largely concentrated on its band and spin structures while its mesoscopic electronic and magnetic response, crucial for future device applications, has not been explored experimentally. Here, we used scanning superconducting quantum interference device microscopy for its sensitivity to both local diamagnetic susceptibility and current distribution in order to image the superfluid density and supercurrent in FST. We found that in FST with 10% interstitial Fe, whose magnetic structure was heavily disrupted, bulk superconductivity was significantly suppressed whereas edge still preserved strong superconducting diamagnetism. The edge dominantly carried supercurrent despite of a very long magnetic penetration depth. The temperature dependence of the superfluid density and supercurrent distribution were distinctively different between the edge and the bulk. Our Heisenberg modeling showed that magnetic dopants stabilize anti-ferromagnetic spin correlation along the edge, which may contribute towards its robust superconductivity. Our observations hold implication for FST as potential platforms for topological quantum computation and superconducting spintronics.