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In this work, we investigate a static and spherically symmetricBardeen-Kiselev black hole with cosmological constant which is a solution ofthe Einstein-non-linear Maxwell field equations along with a quintessentialfield. We compute the quasinormal frequencies for Bardeen-Kiselev blackhole(BH) with cosmological constant due to electromagnetic and gravitationalperturbations. By varying the BH parameters, we discuss the behaviour of bothreal and imaginary parts of the BH quasinormal frequencies and comparefrequencies with Reissner-Nordstr\"om-de Sitter BH surrounded by quintessence(RN-dSQ). Interestingly, it shows that the response of Bardeen-Kiselev BH withcosmological constant and RN-dSQ under electromagnetic perturbations aredifferent when the charge parameter $q$, the state parameter $w$ and thenormalization factor $c$ are varied, but for the gravitational perturbations,the response of Bardeen-Kiselev BH with cosmological constant and RN-dSQ aredifferent only when the charge parameter $q$ is varied. Therefore, comparedwith the gravitational perturbations, the electromagnetic perturbations can beused to understand nonlinear and linear electromagnetic fields in curvedspacetime separately. Another interesting observation is that due to thepresence of quintessence, the electromagnetic perturbations around theBardeen-Kiselev BH with cosmological constant damps faster and oscillatesslowly, and for the gravitational perturbations, the quasinormal mode decaysslowly and oscillates slowly. We also study the reflection and transmissioncoefficients along with absorption cross section for the Bardeen-Kiselev BHwith cosmological constant, it shows that the transmission coefficients willincrease due to the presence of quintessence.

Probing Bardeen-Kiselev black hole with cosmological constant caused by  Einstein equations coupled with nonlinear electrodynamics using quasinormal  modes and greybody bounds