I want to use the built-in FileManagerToolBarSortTool but I want to remove the "Date Modified" option from the "Sort BY" menu.

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ADMIN EDIT

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For the time being, a possible option is to create a custom tool for sorting. You can use the SplitButton component to simulate the built-in UI. Upon selecting option from the dropdown, you may sort your data collection based on the selected custom sort option. Call the Rebind method to refresh the data after updating it.