  In the present work, considering critical gravity as a gravity model, an
electrically charged topological Anti-de Sitter black hole with a matter source
characterized by a nonlinear electrodynamics framework is obtained. This
configuration is defined by an integration constant, three key structural
constants, and a constant that represents the topology of the event horizon.
Additionally, based on the Wald formalism, we probe that this configuration
enjoys non-trivial thermodynamic quantities, establishing the corresponding
first law of black hole thermodynamics, as well as local stability under
thermal and electrical fluctuations. Additionally, via the Gibbs free energy we
note that the topology of the base manifold allows us to compare this charged
configuration with respect to the thermal AdS space-time, allowing us to obtain
a first-order phase transition. The quasinormal modes and the greybody factor
are also calculated by considering the spherical situation. We found that the
quasinormal modes exhibit a straightforward change for variations of one of the
structural constants.
