<p>We study the effect of an external magnetic field on superconducting properties within a mean-field theoretical framework motivated by iron-based superconductors. Inclusion of the magnetic field is introduced solely by Zeeman splitting of quasi-particle energies, corresponding to the Pauli-limited regime, valid in orbital magnetic effects being neglected. Based on the Zubarev Green’s function formalism, the self-consistent equations of the superconducting (SC) order parameter, quasi-particle spectrum, and density of states (DOS) are found. The issue of dependence of the SC gap, DOS and transition temperature on the degree of magnetic field and temperature is analysed in the framework. The findings indicate that the superconductivity was suppressed monotonically with magnetic field and the quasi-particle DOS was subject to Zeeman splitting and its associated changes. The current methodology is not meant to give a quantitative and material-specific description of iron-based superconductors; instead, it provides a qualitative description of the superconducting behaviour of Pauli-limited systems at the mean-field level.</p>