You may not want to disable notifications for the Mail app completely on your iPhone because you might miss important emails when they arrive. However, you can at least mute conversation threads individually. This will not mute all conversations of the same sender, but only the thread you have selected. It also works for group email threads that can get chaotic.
Muting a conversation in Mail works for all threads, but you'll see the biggest benefit when you mute a particularly chatty group email chat that usually alerts you to alarm after alert. Muting threads does not move them in your email app. They remain as usual in the inbox marked as unread. You just do not receive notifications from the Notification Center.
To mute email conversations, you must log in. Running iOS 1
There are two ways to mute an email conversation thread in iOS 13 – swipe from a folder list and tap in the email thread itself.
Option 1: Mute email threads from list view
To use the swipe gesture, open your Inbox or another folder where the conversation is. Then swipe left over the e-mail thread you want to silence to see the available options. If you swipe too far, the message may be deleted, marked, or moved automatically. Finally, tap on the gray "More" button and select "Mute" in the action sheet.
If you're already in the email you want to mute notifications for, touch the Reply button in the lower-right corner. In the action sheet that appears, tap Mute and you're done.
Regardless of how you muted them, you will receive them No more notifications for this email thread. For muted emails, a mute icon (crossed-out bell) will be displayed at the time of each message. This applies both within the email thread and in the list view of any mailbox or folder.