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In the present work, considering critical gravity as a gravity model, anelectrically charged topological Anti-de Sitter black hole with a matter sourcecharacterized by a nonlinear electrodynamics framework is obtained. Thisconfiguration is defined by an integration constant, three key structuralconstants, and a constant that represents the topology of the event horizon.Additionally, based on the Wald formalism, we probe that this configurationenjoys non-trivial thermodynamic quantities, establishing the correspondingfirst law of black hole thermodynamics, as well as local stability underthermal and electrical fluctuations. Moreover, the quasinormal modes and thegreybody factor are also calculated by considering the spherical situation. Wefound that the quasinormal modes exhibit a straightforward change forvariations of one of the structural constants.

Quasinormal modes, greybody factors and thermodynamics of four dimensional AdS black holes in Critical Gravity