In this article we investigate the effects of short-range anti-ferromagnetic correlations on the gap opening of topological Kondo insulators. We add a Heisenberg term to the periodic Anderson model at the limit of strong correlations in order to allow a small degree of hopping of the localized electrons between neighboring sites of the lattice. This new model is adequate for studying topological Kondo insulators, whose paradigmatic material is the compound [Formula: see text]. The main finding of the article is that the short-range antiferromagnetic correlations, present in some Kondo insulators, contribute decisively to the opening of the Kondo gap in their density of states. These correlations are produced by the interaction between moments on the neighboring sites of the lattice. For simplicity, we solve the problem on a two dimensional square lattice. The starting point of the model is the [Formula: see text] ions orbitals, with [Formula: see text] multiplet in the presence of spin-orbit coupling. We present results for the Kondo and for the antiferromagnetic correlation functions. We calculate the phase diagram of the model, and as we vary the [Formula: see text] level position from the empty regime to the Kondo regime, the system develops metallic and topological Kondo insulator phases. The band structure calculated shows that the model describes a strong topological insulator.