  The origin of tiny neutrino mass is an unsolved puzzle leading to a variety
of phenomenological aspects beyond the Standard Model (BSM). Among several
interesting attempts, $U(1)$ gauge extension of Standard Model (SM) is a simple
and interesting set-up where the so-called seesaw mechanism is incarnated by
the addition of three generations of right-handed neutrinos followed by the
breaking of $U(1)$ and electroweak symmetries. Such scenarios are anomaly free
in nature appearing with a neutral BSM gauge boson ($Z^\prime$). In addition to
that, there comes another open question regarding the existence of a
non-luminous, hitherto unidentified object called Dark Matter (DM) originating
from the measurement of its relic density. To explore properties of $Z^\prime$,
we focus on chiral and flavored scenarios where $Z^\prime-$neutrinos
interaction could be probed in the context of cosmic explosions like gamma-ray
burst (GRB221009A, so far the highest energy), blazar (TXS 0506+056) and Active
galaxy (NGC1068) respectively. The neutrino antineutrino annihilation produces
electron-positron pair which could energize GRB through energy deposition.
Taking the highest energy GRB under consideration and estimating the energy
deposition rates we constrain $Z^\prime$ mass $(M_{Z^\prime})$ and the
additional $U(1)$ coupling $(g_X)$ for chiral and flavored scenarios in the
Schwarzchild, Hartle-Thorne and modified gravity frameworks. On the other hand,
adding viable and alternative DM candidates in these models we study
neutrino-DM scattering mediated by $Z^\prime$ in the $t-$ channel and estimate
constraints on $g_X-M_{Z^\prime}$ plane using observed data of high energy
neutrinos from cosmic blazar and active galaxy at the IceCube experiment. We
compare our results with bounds obtained from different scattering, beam-dump
and $g-2$ experiments.
