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We investigate the null geodesics and the shadow cast by the Kerr-Newman-Kiselev-Letelier (KNKL) black hole for the equation of state parameter $\omega_q=-2/3$ and for different values of the spacetime parameters, including the quintessence parameter $\gamma$, the cloud of string (CS) parameter $b$, the spin parameter $a$ and the charge $Q$ of the black hole. We notice that for the increasing values of the parameters $\gamma$ and $b$ the size of the shadow of the KNKL black hole increases and consequently the strength of the gravitational field of the black hole increases. On the other hand with increase in the charge $Q$ of the black hole the size of the shadow of the black hole decreases. Further with the increase in the values of the spin parameter $a$ of the KNKL black hole, we see that the distortion of the shadow of the black hole becomes more prominent. Moreover we use the data released by the Event Horizon Telescope (EHT) collaboration, to restrict the parameters $b$ and $\gamma$ for the KNKL black hole, using the shadow cast by the KNKL black hole. To this end, we also explore the relation between the typical shadow radius and the equatorial and polar quasinormal mods (QNMs) for the KNKL black hole and extend this correspondence to non-asymptotically flat spacetimes. We also study the emission energy rate from the KNKL black hole for the various spacetime parameters, and observe that it increases for the increasing values of both the parameters $\gamma$ and $b$ for fixed charge-to-mass and spin-to-mass ratios of the KNKL black hole. Finally, we investigate the effects of plasma on the photon motion, size and shape of the shadow cast by the KNKL black hole...