The option to control alerts for specific conversations in Skype is only available in Skype on Android (6.0+), Android tablet, iPhone and iPad.
- Tap the contact or group name at the top of the chat window.
- Scroll down to Chat or Group settings.
- Toggle notifications off or on for that chat.
Alternatively for group chats, you can enable Smart notifications so you will only be notified when you are quoted or @mentioned.