As long as you're subscribed to a Substack and have push notifications enabled, you'll receive an app notification about any new posts.
To completely turn off notifications on the Substack iOS app (which means you'll no longer be subscribed to the publication), tap on your profile picture and tap on the Substack you want to stop receiving push notifications and/or emails from.
Then tap on the three dots in the top right corner and tap "Unsubscribe".
Note: Turning off all notifications will unsubscribe you from the publication but will not cancel your subscription if you're a paying subscriber. Learn more here on how to cancel your subscription.