The recent discovery and evidence of neutrino signals from distant sources, TXS 0506+056 and NGC 1068 respectively, provide opportunities to search for rare interactions of neutrinos that they might encounter on their paths. One potential scenario of interest is the interaction between neutrinos and dark matter, which is invisible and expected to be abundantly spread over the Universe. Various astrophysical observations have implied the existence of dark matter. When high-energy neutrinos from extragalactic sources interact with dark matter during their propagation, their spectra might show suppressions at specific energy ranges, where such interactions occur. These attenuation signatures from the interaction might be measurable on Earth with large neutrino telescopes such as the IceCube Neutrino Observatory. This analysis is focused on the search for rare interactions of high-energy neutrinos from the IceCube-identified astrophysical neutrino sources with dark matter in sub-GeV masses and several benchmark mediator cases using the upgoing track-like events. In this poster, sensitivity studies about the interaction of neutrinos and dark matter are presented.