When someone sends you a direct message on Substack, you'll receive a push notification from the Substack app or an email, depending on your notification settings.
By default, notifications for new messages and requests will be turned on.
You can change DM notifications in the Notifications section on the Substack iOS app (Messages section on Android) or your Substack account settings page.
On the web
In the Messaging section on your Substack Settings page, uncheck the "Email" and "Push" boxes next to "Messages" and "Message Requests" to disable receiving notifications for every new message and new message request.
On the Substack app
Click on your profile picture on the Substack iOS app and select the Settings gear icon. Tap on Notifications and select Messaging. Uncheck the "Email" and "Push" boxes next to "New messages" and "New message requests" if you don't want to receive any DM notifications.