You can change your Mail notification settings and choose which mailboxes and email threads to receive notifications from.
To reduce interruptions from busy email threads, you can mute notifications from messages in a conversation.
Go to the Mail app on your iPhone.
Do any of the following:
When reading a message: Tap > Apps > Mail.
Tap Notifications, then make sure that Allow Notifications is on.
Tap Customize Notifications, then tap the email account you want to make changes to.
Select the settings you want, like Alerts or Badges. When you turn on Alerts, you have the option to customize your sounds by changing the alert tone or ringtone.
You can set times when you want to allow notifications from the Mail app. See Flag or block emails in Mail on iPhone