I want to save the notification from specific user in friend list in mysql database using php and twitter api
Twitter has two main APIs. HTTP REST and Stream API so you could do that two ways but I think PHP is only suitable for HTTP API since PHP is not multithreaded.
With PHP and cURL extension you could periodically poll the HTTP Twitter API to look for changes on user you are following.
I would use the Stream API which already has a Java client implemented by Twitter staff that works like a charm and receives the updates in RT. For further details:
REST API: https://dev.twitter.com/rest/public
Streaming API https://dev.twitter.com/streaming/overview
Hosebird (Streaming client by Twitter) https://github.com/twitter/hbc
Hope it helps
The Twitter Account Activity API appears to be the way to do this, now.
"The Account Activity API - All Activities (beta) delivers realtime access to all activities related to a Twitter account via webhooks."
https://developer.twitter.com/en/docs/accounts-and-users/subscribe-account-activity/overview