This may be generational, but yes, notif is used commonly as a stand-in for notification. I would go so far as to say that notif is the one that most people I interact with use primarily, and notification is the pedantic form, like TV vs television.
Note that while notif is a bit more common on social media than it is in spoken language (though I’ve heard it in both), I would call it more slang than abbreviation. Social media and texting has long moved past the point where words were abbreviated just to save typing; notification is no exception. Note that almost all of the extant “texting abbreviations”, e.g. oomf, or lol have specific semantics that long since diverged from those of their long forms.
Also, in response to Mitch’s answer, the short form of notification is most certainly not alert which I have never heard in any context outside of missiles. This is probably for no reason other than Apple deciding to use the word notifications to refer to its lockscreen messages, and the fact that iPhones have the predominant market share among the younger generation.
Note to downvoters: it is difficult to find meaningful evidence regarding the usage of notif and similar slang, especially if you want data on spoken frequency. Standard methods like counting occurrences and frequency of use on Google’s index will be affected by the choice of sample pool more than anything else. notif will naturally be hard to find in say, a search of Google Books, while I would expect it to be predominant on Twitter or iMessage. The former isn’t exactly known for providing credible statistics, the latter is impossible. As with anything regarding slang terms, “personal experience” is the only reliable source.
Although a handful of examples does not prove a trend, here are some public, recent (~1–2 months old) tweets from people that I follow that use notif.
I JUMPED RIGHT OUT OF MY SEAT WHEN I SAW THE NOTIF
WAIT DO YOU GET A NOTIF WHEN PEOPLE DO THAT
idk why but your notif didn’t pop up ???
The important takeaway here is that notification is the only word that’s been “shortened” here†, even though there are a number of typing-saving reductions that could have been used, e.g. people → ppl, you → u, your → ur. The last person has even elected to include a (curly) apostrophe in the word didn’t, a relatively unwieldy character to type on an iPhone keyboard. This indicates that notif was used for reasons other than reducing typing.
† You might have noticed the usage of idk. Without getting too much into the nitty gritty of twitter slang, idk is indeed used as a true abbreviation, but it’s so ubiquitous that it’s essentially the canonical form of I don’t know now which makes it a somewhat special case. idk is also atomic; no one writes dk for don’t know.