This paper investigates the thermodynamic topology of topological black holes in $ F(R) $-ModMax gravity's rainbow, incorporating the effects of high energy and topological parameters. The study combines $ F(R) $ gravity with ModMax nonlinear electrodynamics to analyze black hole solutions and their thermodynamic properties. Black holes are treated as thermodynamic systems, and thermodynamic quantities such as mass, entropy, and temperature are derived. The Hawking temperature and total mass of black holes are found to depend on the topological parameter. The thermodynamic topology is analyzed using the off-shell free energy method, where black holes are considered as defects in their thermodynamic spaces. Two thermodynamic ensembles—fixed charge (q) and fixed potential ($ \phi $) ensembles—are considered. The local and global topology of black holes is studied by calculating topological charges at defects in their thermodynamic spaces. The black holes are classified into three topological classes based on their winding numbers: -1, 0, and 1. The topological classes depend on the value of the rainbow function, the sign of the scalar curvature, and the choice of ensembles. The analysis reveals that the topological charge is invariant under variations of the rainbow function, $ f(\varepsilon) $, $ g(\varepsilon) $, $ \gamma $, and $ f_{R_0} $, while the sign of $ R_0 $ determines the topological charge. For positive $ R_0 $, the topological charge is 0, and for negative $ R_0 $, it is +1. The study also shows that the topological charge is independent of other thermodynamic parameters except for the sign of $ R_0 $. The results highlight the importance of topological parameters in determining the thermodynamic properties and stability of black holes in $ F(R) $-ModMax gravity's rainbow.This paper investigates the thermodynamic topology of topological black holes in $ F(R) $-ModMax gravity's rainbow, incorporating the effects of high energy and topological parameters. The study combines $ F(R) $ gravity with ModMax nonlinear electrodynamics to analyze black hole solutions and their thermodynamic properties. Black holes are treated as thermodynamic systems, and thermodynamic quantities such as mass, entropy, and temperature are derived. The Hawking temperature and total mass of black holes are found to depend on the topological parameter. The thermodynamic topology is analyzed using the off-shell free energy method, where black holes are considered as defects in their thermodynamic spaces. Two thermodynamic ensembles—fixed charge (q) and fixed potential ($ \phi $) ensembles—are considered. The local and global topology of black holes is studied by calculating topological charges at defects in their thermodynamic spaces. The black holes are classified into three topological classes based on their winding numbers: -1, 0, and 1. The topological classes depend on the value of the rainbow function, the sign of the scalar curvature, and the choice of ensembles. The analysis reveals that the topological charge is invariant under variations of the rainbow function, $ f(\varepsilon) $, $ g(\varepsilon) $, $ \gamma $, and $ f_{R_0} $, while the sign of $ R_0 $ determines the topological charge. For positive $ R_0 $, the topological charge is 0, and for negative $ R_0 $, it is +1. The study also shows that the topological charge is independent of other thermodynamic parameters except for the sign of $ R_0 $. The results highlight the importance of topological parameters in determining the thermodynamic properties and stability of black holes in $ F(R) $-ModMax gravity's rainbow.