In this work we present the study of the renormalizability of the Generalized Quantum Electrodynamics (${\mathrm{GQED}}_{4}$). We begin the article by reviewing the on-shell renormalization scheme applied to ${\mathrm{GQED}}_{4}$. Thereafter, we calculate the explicit expressions for all the counter-terms at one-loop approximation and discuss the infrared behavior of the theory as well. Next, we explore some properties of the effective coupling of the theory which would give an indictment of the validity regime of theory: ${m}^{2}\ensuremath{\le}{k}^{2}<{m}_{P}^{2}$. Afterwards, we make use of experimental data from the electron anomalous magnetic moment to set possible values for the theory free parameter through the one-loop contribution of Podolsky mass-dependent term to Pauli's form factor ${F}_{2}({q}^{2})$.