The signals from outer space and their detection have been playing animportant role in particle physics, especially in discoveries of and searchesfor physics beyond the Standard Model (BSM); beyond the evidence of dark matter(DM), for example, the neutrinos produced from the dark matter annihilation isimportant for the indirect DM searches. Moreover, a wide range of new,well-motivated physics models and dark-sector scenarios have been proposed inthe last decade, predicting cosmogenic signals complementary to those in theconventional direct detection of particle-like dark matter. Most notably,various mechanisms to produce (semi-)relativistic DM particles in the presentuniverse (e.g. boosted dark matter) have been put forward, while beingconsistent with current observational and experimental constraints on DM. Theresulting signals often have less intense and more energetic fluxes, to whichunderground, kiloton-scale neutrino detectors can be readily sensitive. Inaddition, the scattering of slow-moving DM can give rise to a sizable energydeposit if the underlying dark-sector model allows for a large mass differencebetween the initial and final state particles, and the neutrino experimentswith large volume detectors are well suited for exploring these opportunities. This White Paper is devoted to discussing the scientific importance of thecosmogenic dark matter and exotic particle searches, not only overviewing therecent efforts in both the theory and the experiment communities but alsoproviding future perspectives and directions on this research branch. Alandscape of technologies used in neutrino detectors and their complementarityis discussed, and the current and developing analysis strategies are outlined.<br
