  In this study, we explore the corrected thermodynamics of non-linear magnetic
charged anti-de Sitter (AdS) black holes surrounded by quintessence,
incorporating thermal fluctuations and deriving the corrected thermodynamic
potentials. We analyze the effects of corrections due to thermal fluctuations
on various thermodynamic potentials, including enthalpy, Helmholtz free energy,
and Gibbs free energy. Our results show significant impacts on smaller black
holes, with first-order corrections destabilizing them, while second-order
corrections enhance stability with increasing parameter values. The specific
heat analysis further elucidates the stability criteria, indicating that the
large black holes ensure stability against phase transitions. However, the
thermal fluctuations do not affect the physical limitation points as well as
the second-order phase transition points of the black hole. Our findings
highlight the intricate role of thermal fluctuations in black hole
thermodynamics and their influence on stability, providing deeper insights into
the behaviour of black holes under corrected thermodynamic conditions.
