I would like to clarify that mobile as well as desktop events are handled internally by Telerik.Web.UI and on that base we provide an API that can be used regardless whether a desktop or mobile browser is used.
For example, a mouse click and a touchscreen device tap over an appointment would result in an OnClientAppointmentClick event that occurs when the user clicks an appointment. A long tap on an appointment would trigger context menu pop-up or AdvancedEdit form to appear, depending on whether you have set a context menu or not. Mobile RadScheduler interaction is described in the Mobile Support section
of RadScheduler documentation.
There are no specific mobile Client-Side API available and there are no samples available on handling mobile events. The whole list of Client-Side RadScheduler events is available in the RadScheduler Client-side Programming help article
If you would like, you could specify what kind of interaction and handling you want to achieve, so we could provide you suggestions on what RadScheduler events could be used in that case.
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