In this paper we study, by means of numerical simulations, the topological properties of $SU(3)$ and $SU(4)$ trace deformed Yang-Mills theory defined on $\mathbb{R}^3\times S^1$, in which center symmetry is recovered even at small compactification radii. In particular, we compute the topological suscpetibility $\chi$ and the coefficient $b_2$ (related to the fourth cumulant of the topological charge distribution). We find that these observables computed in the deformed theory when center symmetry is recovered are compatible with their values at zero temperature both for 3 and 4 colours.