I am building an ionic2 application and I want to enable push notification and I have seen many ways to do it like using firebase and google but I have website and I want to send my notification from my website to the app and I was wondering how to do it do I have to build my own API or something like that I would like to mention also that I have a table for the notification that contains the following fields (message, subject and the address of the device)
Yes you will have to write you own API. Depending on the technology(pHp, nodeJs etc) there variant packages for them.
For nodeJs server side APP check this
For Laravel project
You can google for other technology packages. I hope this helps.