  The investigation of non-vacuum cosmological backgrounds containing black
holes is greatly enhanced by the Kiselev solution. This solution plays a
crucial role in understanding the properties of the background and its
relationship with the features of the black hole. Consequently, the
gravitational memory effects at large distances from the black hole offer a
valuable means of obtaining information about the surrounding field parameter N
and parameters related to the hair of the hairy Kiselev Black hole. This paper
investigates the gravitational memory effects in the context of the Kiselev
solution through two distinct approaches. At first, the gravitational memory
effect at null infinity is explored by utilizing the Bondi-Sachs formalism by
introducing a gravitational wave (GW) pulse to the solution. The resulting
Bondi mass is then analyzed to gain further insight. Therefore, the Kiselev
solution is being examined to determine the variations in Bondi mass caused by
the pulse of GWs. The study of changes in Bondi mass is motivated by the fact
that it is dynamic and time-dependent, and it measures mass on an
asymptotically null slice or the densities of energy on celestial spheres. In
the second approach, the investigation of displacement and velocity memory
effects is undertaken in relation to the deviation of two neighboring geodesics
and the deviation of their derivative influenced by surrounding field parameter
N and the hair of hairy Kiselev black hole. This analysis is conducted within
the context of a gravitational wave pulse present in the background of a hairy
Kiselev black hole surrounded by a field parameter N.
