Alternatively, you can turn your Notifications for conversations off to stop all chat notifications in the new Skype. From the Chats screen, tap your profile picture > Notifications for conversations button > Turn Off.
Yes, you can control alerts for specific conversations in Skype.
There could be a few reasons why you might not be receiving notifications:
If you close the Skype app without signing out first, you might still receive notifications. If you want to stop these notifications, you can either disable them from your Settings or sign out before you close the app.
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