This paper investigates the thermodynamic topology of static, charged static, and charged rotating black holes in the context of $f(R)$ gravity. The authors use the generalized off-shell free energy method to study the local and global topology of these black holes by computing winding numbers at topological defects. For static black holes, the topological charge is found to be consistently $-1$ across different $f(R)$ models and thermodynamic parameters. For charged static black holes, the topological charge is zero in the fixed charge ensemble and $-1$ in the fixed potential ensemble, and it remains unchanged with variations in the charge and curvature radius. For charged rotating black holes, the topological charge varies depending on the ensemble: $1$ in the fixed $(q, J)$ ensemble, $1$ or $0$ in the fixed $(q, \Omega)$ ensemble, and $-1, 0, 1$ in the fixed $(\Omega, \phi)$ ensemble, depending on the values of the scalar curvature, angular frequency, and potential. The study concludes that the thermodynamic topologies of charged static and charged rotating black holes are influenced by the choice of ensemble and the thermodynamic parameters.This paper investigates the thermodynamic topology of static, charged static, and charged rotating black holes in the context of $f(R)$ gravity. The authors use the generalized off-shell free energy method to study the local and global topology of these black holes by computing winding numbers at topological defects. For static black holes, the topological charge is found to be consistently $-1$ across different $f(R)$ models and thermodynamic parameters. For charged static black holes, the topological charge is zero in the fixed charge ensemble and $-1$ in the fixed potential ensemble, and it remains unchanged with variations in the charge and curvature radius. For charged rotating black holes, the topological charge varies depending on the ensemble: $1$ in the fixed $(q, J)$ ensemble, $1$ or $0$ in the fixed $(q, \Omega)$ ensemble, and $-1, 0, 1$ in the fixed $(\Omega, \phi)$ ensemble, depending on the values of the scalar curvature, angular frequency, and potential. The study concludes that the thermodynamic topologies of charged static and charged rotating black holes are influenced by the choice of ensemble and the thermodynamic parameters.