  In this study, we investigate the thermodynamic topology of the Kerr-Sen-Ads
black hole in restricted phase space. In the restricted phase space, a new
parameter, central charge $C$, and its conjugate parameter $\mu$ are
introduced, omitting the well-known $PdV$ term in the first law of black hole
thermodynamics. We study the local and global topology of the black hole by
considering the black hole solution as topological defects in the free energy
landscape. We compute the winding number and the total topological number at
the thermodynamic defects. For our analysis, we have considered five ensembles
of Kerr-Sen-Ads black holes in restricted phase space: fixed $(Q, J, C)$, fixed
$(\phi, J, C)$, fixed $(Q,\Omega, C)$, fixed $(Q, J, \mu)$, and fixed
$(\phi,\Omega, C)$, where $Q$ is the electric charge, $J$ is the angular
momentum, $C$ is the central charge, $\phi$ is the electric potential conjugate
to charge, $\Omega$ is the angular frequency conjugate to $J$, and finally,
$\mu$ is the chemical potential. In the fixed $(Q, J, C)$, fixed $(\phi, J,
C)$, and fixed $(Q, J, \mu)$ ensembles, we find a topological charge of $+1$.
In the fixed $(Q,\Omega, C)$ and fixed $(\phi, \Omega, C)$ ensembles, depending
on the values of the thermodynamic parameters, we find topological charges of
$-1$, $0$, and $+1$. Interestingly, in ensembles where we find the topological
charge to be $0$, we observe both Hawking-Page and Davies type phase
transitions. We show that both types of these phase transitions can be studied
using a common vector field, and the topological charges associated with Davies
type and Hawking-Page phase transitions are $-1$ and $+1$, respectively.
