Many people use Gmail, and many people use Gmail on their iOS devices through the stock Mail application. Unfortunately as of January 30, 2013, Google no longer supports push notifications for new devices that set up Gmail accounts. Instead, Google offers a Gmail application in the App Store
for free that offers push notifications instead.
If you want to add push notifications to your Mail application for your Gmail account again rather than having to use another e-mail client to handle your Gmail inbox, you can now use a new jailbreak tweak called Push for Gmail
by iOS developer Noppers Software.
The tweak uses the Gmail application from Google to utilize push notifications in the Mail application. To use the tweak, make sure you download the Gmail application from the App Store and set up your Gmail account. Next, you will need to set up the same Gmail account in the Mail application from Apple. Once that’s done, set your Gmail account via the Mail application to “Fetch” instead of push and set the schedule to “manually.” Finally, respring your iOS device and you should now start receiving push notifications for Gmail through Apple's Mail application.
Unfortunately since the tweak utilizes the Gmail application to supply you with push notifications for the Mail application, you won’t be able to delete the Gmail application after configuring both of your e-mail clients. On the other hand, you can use another tweak like Springtomize 2 to hide the Gmail application icon from the home screen, or you can just add it to a folder. If you delete the Gmail application, you will no longer receive push notifications for your Gmail inbox in Apple's Mail application.
Because the tweak adds push notifications back to the Mail application for Gmail accounts, you will be able to have all of your inboxes in your Mail application so they’re all easily accessible from the same place without having to open and close more than one e-mail client application. So it really makes things a lot more convenient for the user in the long run.
If you want to give the tweak a try, you can find Push for Gmail in Cydia's ModMyi repository for just 99¢.
Push for Gmail