Experimental evidence of novel phenomena in hydrogenated graphite fibers is found. An indirect excitonic mechanism is likely leading to a SC state below the temperature Tc = 50 K, where the gap is divergent. Analysis of the gap within the framework provided by the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity shows that this is a multigap system. The energy gap data can be better explained within the framework of topologically protected flat bands applied to systems in which superconductivity occurs on the surface or at the internal interfaces of the samples. The temperature dependence of the SC gap is linear above 50 K. We use nonlocal differential conductance Gdiff(V) = dI(V)/dV experimental data to show clear evidence of topological phenomena such as interference of chiral asymmetric Andreev edge states and crossed Andreev conversion. Gdiff(V) has a negative part that results from the nonlocal coherence between electron and holes in the Andreev edge states. We conclude that hydrogenated graphite bears the marks of an unconventional high-temperature superconductor (HTSC).