This paper investigates the thermodynamic topology of black holes in $ f(R) $ gravity, focusing on static, charged static, and rotating charged black holes. The thermodynamic topology is analyzed using the off-shell free energy method, treating black holes as topological defects in their thermodynamic spaces. The local and global topology of these black holes is determined by computing winding numbers at these defects. For static black holes, three different $ f(R) $ models are considered. The topological charge for a static black hole is always -1, independent of thermodynamic parameters and the choice of $ f(R) $ model. For charged static black holes, the topological charge is zero in the fixed charge ensemble and -1 in the fixed potential (φ) ensemble. For rotating charged black holes, the topological charge varies depending on the ensemble: 1 in the fixed (q, J) and (φ, J) ensembles, 1 or 0 in the fixed (q, Ω) ensemble, and -1, 0, or 1 in the fixed (Ω, φ) ensemble. The thermodynamic topology of rotating charged black holes is influenced by both the choice of ensemble and the thermodynamic parameters. The study shows that the thermodynamic topology of black holes in $ f(R) $ gravity is sensitive to the ensemble used and the thermodynamic parameters. The topological charge, which classifies black holes into different topological classes, is determined by the winding numbers around the defects in the thermodynamic space. The results highlight the importance of ensemble selection in understanding the thermodynamic properties and phase transitions of black holes in modified gravity theories.This paper investigates the thermodynamic topology of black holes in $ f(R) $ gravity, focusing on static, charged static, and rotating charged black holes. The thermodynamic topology is analyzed using the off-shell free energy method, treating black holes as topological defects in their thermodynamic spaces. The local and global topology of these black holes is determined by computing winding numbers at these defects. For static black holes, three different $ f(R) $ models are considered. The topological charge for a static black hole is always -1, independent of thermodynamic parameters and the choice of $ f(R) $ model. For charged static black holes, the topological charge is zero in the fixed charge ensemble and -1 in the fixed potential (φ) ensemble. For rotating charged black holes, the topological charge varies depending on the ensemble: 1 in the fixed (q, J) and (φ, J) ensembles, 1 or 0 in the fixed (q, Ω) ensemble, and -1, 0, or 1 in the fixed (Ω, φ) ensemble. The thermodynamic topology of rotating charged black holes is influenced by both the choice of ensemble and the thermodynamic parameters. The study shows that the thermodynamic topology of black holes in $ f(R) $ gravity is sensitive to the ensemble used and the thermodynamic parameters. The topological charge, which classifies black holes into different topological classes, is determined by the winding numbers around the defects in the thermodynamic space. The results highlight the importance of ensemble selection in understanding the thermodynamic properties and phase transitions of black holes in modified gravity theories.