  In this paper we investigate, by means of numerical lattice simulations, the
topological properties of the trace deformed $SU(3)$ Yang-Mills theory defined
on $S_1\times\mathbb{R}^3$. More precisely, we evaluate the topological
susceptibility and the $b_2$ coefficient (related to the fourth cumulant of the
topological charge distribution) of this theory for different values of the
lattice spacing and of the compactification radius. In all the cases we find
results in good agreement with the corresponding ones of the standard $SU(3)$
Yang-Mills theory on $\mathbb{R}^4$.
