  We investigate thermodynamics and geometrothermodynamics of regular Bardeen
AdS black hole with quintessence. The thermodynamics of the black hole is
studied using temperature-entropy ($T-S$) , Pressure-Volume ($P-v$), and Gibbs
energy plots, which indicate a critical behaviour.This is also confirmed from
the divergence of specific heat against entropy, which shows a second-order
phase transition. Moreover, we observe that the quintessence state parameter
$\omega$ shifts the transition point to lower entropy values. Using the concept
of thermodynamic Ruppeiner and Weinhold geometry, we calculated the
thermodynamic curvature scalar $R_R$ and $R_W$ in the quintessence dark energy
regime ($\omega =-2/3$). While these curvature scalars enable us to identify
the critical behavior, they do not show divergence at the phase transition
points observed in specific heat studies. To resolve this puzzle, we have
adopted the method of geometrothermodynamics proposed by Hernando Quevedo.
Choosing a Legendre invariant Quevedo metric, the curvature scalar $R_Q$ shows
singularity at the same point as seen in the specific heat divergence.
