The theoretical aspects of research on the role of Jahn–Teller (JT) interactions in quasi-two-dimensional iron-based high-[Formula: see text] superconductors are analyzed. A model Hamiltonian for the JT distortion in iron-based superconductors is proposed by a tight-binding two-orbital model. We have proposed here a [Formula: see text]-wave pairing symmetry of the form [Formula: see text] in the model in mean-field approximation. The model is solved by Zubarev’s double-time Green’s function technique to find the self-consistent gap equation and is solved self-consistently. The lattice strain energy, specific heat, conduction electron density of states and energy band structure for the system are calculated.