  In this article, we study the particle dynamics around a static and
spherically symmetric Bardeen-Kiselev black hole (BK BH) which is a solution of
the Einstein-non-linear Maxwell field equations along with a quintessential
field. We discuss its essential geometrical properties such as scalar
invariants and size of innermost stable circular orbits. Dynamics of test
particles around the BH is also studied. Moreover, we also computed the
fundamental frequencies of a test particle orbiting the BH in a slightly
perturbed orbit. Further, the degeneracy relations between the spin of rotating
Kerr BH and magnetic charge of the BK BH at the values of the quintessential
parameter $\omega_q=-1/3$ and in terms of the same values of innermost stable
circular orbits (ISCOs) radius, energy efficiency, twin-peaks quasiperiodic
oscillations (QPOs) frequencies and impact parameter for photon are also
discussed in detail. Finally, we have investigated the relationship between the
shadow radius and the real part of the quasinormal mode (QNM) frequency.
