Do you experience the reported issue in the live demos of RadDatePicker and RadTimePicker - https://demos.telerik.com/aspnet-ajax/datepicker/overview/defaultcs.aspx?skin=Bootstrap
If the issue happens only inside your project, it is most likely due to some custom CSS that breaks the appearance of the controls. You can examine the page with the Inspector and see which CSS selectors override the built-in classes of the controls.
If you are unable to solve the issue, can you provide a live URL to the problematic page or a simple runnable project where the problem can be reproduced?
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