Can I get push notifications for emails in my Gmail Priority Inbox only?

After days of searching I have found the solution. https://www.ultimatenotifier.com/

1. You have to buy Ultimate Notifier from the AppStore. $2.99 at the moment.
2. Create a free account on their site or through the app.
3. Login to the web interface on your computer and under Add Notification select Add Gmail / Google Mail - NEW Priority Inbox
4. Complete the fields username and password with your Gmail username and password. (I know this is a BIG leap of faith.)
5. Save.
6. Log in to the app on your iPhone to receive push notifications

You can do this with MailMinder on an iPhone. Just set up a Source of Gmail with the folder set to the Priority Inbox, then set up a Minder with a Subject of ... This will match any message that has a subject with 3 characters. I know the developer is planning to have a button to match anything in the next release.

Mail Minder has a free mode if you don't mind ads.