The paper explores the thermodynamic topology of topological black holes in $F(R)$-ModMax gravity's rainbow, a modified theory of gravity that includes nonlinear electrodynamics. The authors first derive topological black hole solutions by combining $F(R)$ gravity with ModMax nonlinear electrodynamics. They then analyze these solutions as thermodynamic systems, examining thermodynamic quantities and the first law of thermodynamics. The topological parameter significantly affects the Hawking temperature and total mass of the black holes. The thermodynamic topology is studied using the off-shell free energy method, where black holes are treated as defects in their thermodynamic spaces. Two ensembles, fixed $q$ and fixed $\phi$, are considered to investigate the local and global topology of the black holes. The topological charges at the defects in their thermodynamic spaces are calculated, leading to the classification of black holes into three topological classes based on their winding numbers. The topological classes depend on the value of the rainbow function, the sign of the scalar curvature, and the choice of ensembles. The study reveals that large black holes belong to the class with a negative topological constant ($k = -1$), while small and large black holes have positive mass, electric charge, $\gamma$, $f_{R0}$, and $g(\varepsilon)$ but lower $f(\varepsilon)$. The radius of the event horizon is more sensitive for $k = +1$ compared to other values of the topological constant. The paper also discusses the behavior of the temperature and mass in the high-energy limit and asymptotic behavior, showing that the temperature can be positive for large black holes under certain conditions. The first law of thermodynamics is satisfied for the obtained black hole solutions.The paper explores the thermodynamic topology of topological black holes in $F(R)$-ModMax gravity's rainbow, a modified theory of gravity that includes nonlinear electrodynamics. The authors first derive topological black hole solutions by combining $F(R)$ gravity with ModMax nonlinear electrodynamics. They then analyze these solutions as thermodynamic systems, examining thermodynamic quantities and the first law of thermodynamics. The topological parameter significantly affects the Hawking temperature and total mass of the black holes. The thermodynamic topology is studied using the off-shell free energy method, where black holes are treated as defects in their thermodynamic spaces. Two ensembles, fixed $q$ and fixed $\phi$, are considered to investigate the local and global topology of the black holes. The topological charges at the defects in their thermodynamic spaces are calculated, leading to the classification of black holes into three topological classes based on their winding numbers. The topological classes depend on the value of the rainbow function, the sign of the scalar curvature, and the choice of ensembles. The study reveals that large black holes belong to the class with a negative topological constant ($k = -1$), while small and large black holes have positive mass, electric charge, $\gamma$, $f_{R0}$, and $g(\varepsilon)$ but lower $f(\varepsilon)$. The radius of the event horizon is more sensitive for $k = +1$ compared to other values of the topological constant. The paper also discusses the behavior of the temperature and mass in the high-energy limit and asymptotic behavior, showing that the temperature can be positive for large black holes under certain conditions. The first law of thermodynamics is satisfied for the obtained black hole solutions.