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In the present paper, we investigate the required anisotropy of an exact regular Bardeen black hole characterized by its mass $M$, the nonlinear parameter $g$, the quintessence field parameter $a$ in anti-de sitter spacetime with a static quintessence matter field. We also show that the relative pressure anisotropy, equation of state and the pressure depends on radial coordinate, reflecting the required anisotropy for Bardeen black hole in the quintessence background. Next, we analyze the Joule-Thompson ($JT$) expansion of the black hole spacetime. Treating the cosmological constant as thermodynamic pressure $P$ and its conjugate quantity as thermodynamic volume $V$ we derive the equation of state connecting Hawking temperature and various black hole parameters. We study the $JT$ expansion in the regular Bardeen AdS black holes in the quintessence background through the analysis of inversion temperature and isenthalpic curves. We derive the $JT$ coefficient $μ$, and use them to plot the inversion and isenthalpic curves. We discuss the effect of quintessence parameter $a$ and $ω_q$ on the $JT$ coefficient and inversion temperature, especially with the case of $ω_q=-1$ and $ω_q=-\frac{1}{3}$. Our analysis shows that quintessence dark energy affects the inversion point $(T_i,P_i)$ .