  By considering the concept of a unified single fluid model, referred to as
the modified Chaplygin gas (MCG), which amalgamates dark energy and dark
matter. In this study, we explore the thermodynamic characteristics of charged
anti-de Sitter (AdS) black holes existing in an unconventional fluid
accompanied by MCG. To accomplish this objective, we derive the equations of
state by regarding the charge $Q^{2}$ as a thermodynamic variable. The impact
of MCG parameters on the critical thermodynamic quantities ($\psi_{c}$,
$T_{c}$, $Q_{c}^{2}$) are examined, followed by a detailed analysis of the
$Q^{2}-\psi$ diagram. To provide a clearer explanation of the phase transition,
we present an analysis of the Gibbs free energy. It is important to note that
if the Hawking temperature exceeds the critical temperature, there is a
distinct pattern observed known as swallowtail behavior. This indicates that
the system undergoes a first-order phase transition from a smaller black hole
to a larger one. The critical exponent of the system is found to be in complete
agreement with that of the van der Waals fluid system. Furthermore, we
investigate the impact of MCG parameters and black hole charge on the
Joule-Thomson (J-T) expansion in the extended phase space. The J-T coefficient
is examined to pinpoint the exact region experiencing cooling or heating, the
observation reveals that the presence of negative heat capacity results in the
occurrence of a cooling process. In addition, it is worth noting that the
certain parameters exert a significant influence on the ratio
$\frac{T_{min}}{T_{c}}$. The parameters $\gamma$ and $\beta$ have a
non-negligible effect on the isenthalpy curve.
