  In this work we investigate corrections of the quintessence regime of the
dark energy on the Joule-Thomson (JT) effect of the Reissner Nordstr\"om anti
de Sitter (RNAdS) black hole. The quintessence dark energy has equation of
state as $p_q=\omega\rho_q$ in which $-1<\omega<-\frac{1}{3}.$ Our calculations
are restricted to ansatz: $\omega=-1$ (the cosmological constant regime) and
$\omega=-\frac{2}{3}$ (quintessence dark energy). To study the JT expansion of
the AdS gas under the constant black hole mass, we calculate inversion
temperature $T_i$ of the quintessence RNAdS black hole where its cooling phase
is changed to heating phase at a particular (inverse) pressure $P_i.$ Position
of the inverse point $\{T_i,P_i\}$ is determined by crossing the inverse curves
with the corresponding Gibbons-Hawking temperature on the T-P plan. We
determine position of the inverse point verse different numerical values of the
mass $M$ and the charge $Q$ of the quintessence AdS RN black hole. The
cooling-heating phase transition (JT effect) is happened for $M>Q$ in which the
causal singularity is still covered by the horizon. Our calculations show
sensitivity of the inverse point $\{T_i,P_i\}$ position on the T-P plan to
existence of the quintessence dark energy just for large numerical values of
the AdS RN black holes charge $Q$. In other words the quintessence dark energy
dose not affects on position of the inverse point when the AdS RN black hole
takes on small charges.
