To expand on this a bit, yes, you can configure your settings to get an "alert" (via a notification that appears next to the bell icon in the top right corner of the page, or via a push notification to your device) only when your post has been replied to via the quote feature, or when your username is mentioned with the @ character.
However, it's just an alert — there is currently no way to get an email notification if your post is quoted by someone else.
In other words, when it comes to email notifications, you can either get them for new thread replies or not. The feature does not allow for any more nuance than that. Only the built-in alerts system allows for such fine-grained control.