  The topological Hall effect (THE), given by a composite of electric and
topologically non-trivial spin texture is commonly observed in magnetic
skyrmion crystals. Here we present a study of the THE of electrons coupled to
antiferromagnetic Skyrmion lattices (AF-SkX). We show that, in the strong Hund
coupling limit, topologically non-trivial phases emerge at specific fillings.
Interestingly, at low filling an external field controlling the magnetic
texture, drives the system from a conventional insulator phase to a phase
exhibiting THE. Such behavior suggests the occurrence of a topological
transition which is confirmed by a closing of the bulk-gap that is followed by
its reopening, appearing simultaneously with a single pair of helical edge
states. This transition is further verified by the calculation of the the Chern
numbers and Berry curvature. We also compute a variety of observables in order
to quantify the THE, namely: Hall conductivity and the orbital magnetization of
electrons moving in the AF-SkX texture.
