You can turn off game notifications completely in your device settings.

For iOS devices:
1. Open Settings.
2. Find Fishdom in the application list and select it.
3. Go to Notifications (right side of the screen) and turn off Allow Notifications.

For Android and Amazon Kindle devices:
1. Open Settings -> Applications.
2. Find Fishdom in the list of installed apps and select it.
3. Untick Notifications.