  This study is centered on precisely calculating analytical critical points
for rotating Bardeen-AdS black holes, examining scenarios with and without
external dark field contributions. Importantly, this study represents the
inaugural attempt to address the computation of critical points specifically
for this category of black holes. Our primary focus is on investigating the
impact resulting from variations in the charge of nonlinear electrodynamics on
the critical phenomena of rotating Bardeen black holes, incorporating the
influence of quintessence field contributions. The analytical investigation is
concentrated on the horizon radius, employing two distinct approaches to
simplify the complexity and length of the calculations. Furthermore, our
examination extends to deciphering the intricate relationship between dark
energy and critical phenomena. This includes visually portraying a range of
critical behaviors while detailing a recent discovery regarding how the
intensity of quintessence affects phase transitions. The shifts in these
transitions conform to either a concave or convex function, a characteristic
dependent on the sign of quintessence intensity.
