The response of a QCD-like gauge theory, holographically dual to a deformed $mathrm{AdS}_5$ model, to constant electromagnetic fields is thoroughly investigated. The calculations in this paper are performed for three different cases, i.e., with only a quadratic correction, with only a logarithmic correction, and with both quadratic and logarithmic corrections, for which the parameters are chosen as the ones found in cite{quadlog} by fitting to experimental and lattice results. The critical electric fields of the system are found by analyzing its total potential. Comparing the total potential for the three cases, we observe that the quarks can be liberated easier in quadratic and then logarithmic case, for a given electric field. Then, by calculating the expectation value of a circular Wilson loop, the pair production rate is evaluated while a constant electric field as well as a constant magnetic field are present. The aforementioned result obtained from the potential analysis is also confirmed here when no magnetic fields are present. We moreover find that the presence of a magnetic field perpendicular to the direction of the electric field suppresses the rate of producing the quark pairs and accordingly increases the critical electric field below which the Schwinger effect does not occur. Interestingly, the presence of a parallel magnetic field alone does not change the response of the system to the external electric field, although it enhances the creation rate when a perpendicular magnetic field is also present.
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