  We study the thermodynamic topology of four dimensional dyonic
Anti-de-Sitter(AdS) black hole in three different ensembles: canonical, mixed
and grand canonical ensemble. While canonical ensemble refers to the ensemble
with fixed electric and magnetic charges, mixed ensemble is an ensemble where
we fix magnetic charge and electric potential. In the grand canonical ensemble,
potentials corresponding to both electric and magnetic charges are kept fixed.
In each of these ensembles, we first compute the topological charges associated
with critical points. We find that while in both canonical and mixed ensembles,
there exists one conventional critical point with topological charge $-1$, in
the grand canonical ensemble, we find no critical point. Then, we consider the
dyonic AdS black hole as topological defects in thermodynamic space and study
its local and global topology by computing the winding numbers at the defects.
We observe that while the topologies of the black hole in canonical and mixed
ensembles are identical with total topological charge equaling $1$, in the
grand canonical ensemble, depending on the values of potentials, the total
topological charge is either equal to $0$ or $1$. In canonical and mixed
ensembles, either one generation and one annihilation points or no
generation/annihilation points are found. In the grand canonical ensemble,
depending on the values of potentials, we find either one generation point or
no generation/annihilation point. Thus, we infer that the topological class of
$4$D dyonic AdS black hole is ensemble dependent.
