The Kondo insulator SmB6 has long been known to exhibit low-temperature transport anomalies whose origin is of great interest. Here we uniquely access the surface electronic structure of the anomalous transport regime by combining state-of-the-art laser and synchrotron-based angle-resolved photoemission techniques. We observe clear in-gap states (up to ~4 meV), whose temperature dependence is contingent on the Kondo gap formation. In addition, our observed in-gap Fermi surface oddness tied with the Kramers' point topology, their coexistence with the two-dimensional transport anomaly in the Kondo hybridization regime, as well as their robustness against thermal recycling, taken together, collectively provide strong evidence for protected surface metallicity with a Fermi surface whose topology is consistent with the theoretically predicted topological Fermi surface. Our observations of systematic surface electronic structure provide the fundamental electronic parameters for the anomalous Kondo ground state of correlated electron material SmB6.