Push Specific Folders With iCloud Mail
If you have an IMAP or Exchange account set up, you have control over which folders are pushed to the Mail app. Changes made to those folders on the server are pushed to your iPhone. In addition, you can select the folders you want to push to your iPhone from your iCloud email account, and set up a schedule for fetching those you don’t need to have pushed. When you set up the Mail app on your iPhone, your first mail account was probably iCloud Mail. You can make changes to the folders you have pushed to the phone at any time. Here’s how: The folders you checked sync promptly with the iPhone. You can set the rest of the folders to sync every 15 or 30 minutes, hourly, or manually in the Fetch New Data screen. These folders sync in the background when the iPhone is powered up and has a Wi-Fi connection.
Push Specific Folders With an Exchange Account
If you have an Exchange account set up on your iPhone, you can choose which folders to push to your device from the settings.
Push Folders for IMAP Accounts
For you to sync specific email folders on an IMAP account, your email provider must support the feature. Gmail, for example, lets you pick which labels to show in IMAP accounts, meaning that if you hide those labels, they won’t show up on your iPhone. However, you can’t do this from your phone. Using Gmail as an example, log in to your account in a web browser and access the Labels area of the settings. From there, uncheck labels to prevent those folders from syncing to the Mail app on your phone.