Oh, you mean if you “Enable Mobile Notifications” on some profile on Twitter? In that case, if you use your own Access Token and lookup / show a user - the User will have a
So you could get all the accounts you’re following with /friends/ids, look up all users with /users/lookup and check for “notifications” property on each - once you have a set of users you want notifications for, you can do whatever you want.
You can make your own custom “notification” for your self, with your UserStream https://dev.twitter.com/streaming/userstreams#Data_from_accounts_the_user_follows - and implement a check for retweets or tweets or replies or some other condition, from accounts that you are following and that have
"notification":true (I think the user stream will send a user object along with a tweet, so you don’t need to lookup the user for every tweet in your home timeline)