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In the past decade, the precise measurement of the lastly known neutrino mixing angle $θ_{13}$ has enabled the resolution of neutrino mass hierarchy (MH) at medium-baseline reactor neutrino oscillation (MBRO) experiments. On the other hand, recent calculations of the reactor neutrino flux predict percent-level sub-structures in the $\barν_e$ spectrum due to Coulomb effects in beta decay. Such fine structure in the reactor spectrum could be an important issue for the determination of neutrino MH for the MBRO approach since they could affect the sub-dominant oscillation pattern used to discriminate different hierarchies. Inconveniently, the energy resolutions of current reactor experiments are not sufficient to measure such fine structure, and therefore the size and location in energy of these predicted discontinuities has not been confirmed experimentally. There has been speculation that a near detector is required with sufficient energy resolution to resolve the fine structure such that it can be accounted for in any analysis which attempts to discriminate the MH. This article studies the impact of fine structure on the resolution of MH, based on the predicted reactor neutrino spectra, using the measured spectrum from Daya Bay as a reference. We also investigate whether a near detector could improve the sensitivity of neutrino MH resolution using various assumptions of near detector energy resolution.