I develop a SIP app in iOS and I would like to know if anybody have found a sip server that supports PushKit. It might be
The SIP server doesn't need to support PushKit, this is something in iOS. There are 2 types of push notifications that the app can recognize and handle differently. Through the Apple developers portal you will need to generate a certificate type of Voip Services. Use this and the token while pushing and in iOS register and lookout for these. This site shows differences between push types: https://zeropush.com/guide/guide-to-pushkit-and-voip Apples best practices for VoIP: https://developer.apple.com/library/ios/documentation/Performance/Conceptual/EnergyGuide-iOS/OptimizeVoIP.html
On your SIP server, you will just need to send a push notification on an incoming call. If you use Asterisk you can use AGI so you can perform the push in whichever language. I've always just use APNS but there's a bunch to choose from like AWS, Urban Airship, Onesignal.