iOS don’t support the W3C Spec web push notifications yet. But there is a Safari specific API for web notifications. Refer to this answer on multiple options you have.
https://stackoverflow.com/a/49803408/1057093
Update: Corrected the Answer in the above link to clarify proprietary solution is only for OS X – Safari and no solution for iOS Safari yet. Custom in app notification is the best we can do today for iOS Safari.