Hi @Anonymous ,
Do you want the employees to be able to book Tuesday's and Thursday's in DatePicker, and disable other weekdays, right?
If you want the employees to be able to book Tuesday's and Thursday's in DatePicker, and disable other weekdays, I afraid that there is no way to achieve your needs using the native DatePicker control in your canvas app.
As an alternative solution, you could consider custom a DatePicker control in your app, then you could disable the weekdays within the custom DatePicker based on your needs.
I have customized a DatePicker in my app, and disable other weekdays in it except the Tuesday and Thursday. the screenshot as below:


Set the DisplayMode property of the Title2 inside the MonthDayGallery1 to following:
If(
Weekday(DateAdd(_firstDayInView, ThisItem.Value, Days)) = 3 || Weekday(DateAdd(_firstDayInView, ThisItem.Value, Days)) = 5,
DisplayMode.Edit,
DisplayMode.Disabled
)
More details about customizing DatePicker control in PowerApps, please check the following article:
https://docs.microsoft.com/en-us/archive/blogs/davidni/building-an-interactive-calendar-view-with-powerapps
I have attached my sample custom DatePicker app below, please consider refer to it. When you want to reference the selected date value from the custom datepicker control, please reference value through the _dateSelected variable directly.
Best regards,