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Your requirement of customizing Schedule month cell background color can be achieved using OnMonthCellLoadedEvent of Schedule. Using MonthCellLoadedEventArgs of this event, you can get the Date and Appointment details of the specific date, so that using CellStyle property you can customize the cell.
Please refer the following User Guide documentation to customize the month cell using CellStyle,
You can also pass the Custom view to the entire month cell using OnMonthCellLoadedEvent of Schedule or setting MonthCellTemplate of Schedule MonthViewSettings.
refer our online user guide documentation for the same by the below link,
You can also refer our knowledge base (KB) about displaying the appointment details in month view by referring the following links,
We hope this helps. Please let us know, if you require any further assistance.
Subburaj Pandian V