The IceCube experiment is a cubic kilometer neutrino observatory at the South Pole which uses an array of Digital Optical Modules (DOMs) deep inside the ice to detect neutrinos. IceCube has a denser geometry of DOMs at its bottom central region, DeepCore, which enables it to detect GeV energy atmospheric neutrinos. DeepCore provides a unique avenue to explore various subtle effects related to Beyond the Standard Model (BSM) physics with its high statistics data. In this work, we consider a minimal anomaly-free extension of the Standard Model by an additional lepton-number symmetry ( \(L_e - L_\mu \) or \(L_e - L_\tau \) ), which can introduce a very light gauge boson mediating flavor-dependent neutral current long-range interaction. This new interaction may lead to significant modifications in neutrino oscillation probabilities, which can be observed in the atmospheric neutrino oscillations data at DeepCore. In this contribution, we present the sensitivity of IceCube DeepCore to probe this flavor-dependent long-range interaction potential with a runtime of 9.3 years.