For this you need to manage Planner notifications.
1. First, select the Settings button near the top right of the screen, and then select Notifications.
2. Now in the Notifications dialog box, check the boxes in front the following options:
a. Someone assigns a task to me (Email, Teams, and Mobile Push)
b. A task assigned to me is late, due today, due in next 7 days (Email only)
3. Now click on Save.
You can uncheck the same boxes for turning off the notifications.