iOS Mail doesn't implement it, instead doing a poll every 15 minutes. However it also implements a separate push system which allows true push if the server supports it. The details on how to support this aren't public information.
We talked to Apple, and they were kind enough to give us access to this system. We implemented it on our side, and now when an email arrives at FastMail we can immediately signal to Mail.app that there's new mail available.
What I imagine, though, is a system similar to GCM, which would be not very helpful.
From skimming the notes it looks like it's essentially a way to send APNS notifications to Mail.app and requires a cert from Apple. You could run it from your VPS once you get the cert.
Disclosure: have family connection to owners.
> iOS Mail doesn't implement it, instead doing a poll every 15 minutes. However it also implements a separate push system which allows true push if the server supports it. The details on how to support this aren't public information.
"The details on how to support this aren't public information." My biggest computer-related fears summarized in a single sentence.