I got the #1 issue of a comic magazine called "The Amazing Spider-Man". The publication date is December(!) 2015.
This comes after the previous "Amazing Spider-Man" stopped, as most Marvel comics did, for the big event called "Secret Wars".
As far as I can tell, the story continues from the last "volume",
where Peter has his own company.
Given the above, it would seem it's Earth-616. However that Earth is supposed to have been destroyed during SW.
At the same time, Nick Fury appears in the comic and he looks like Samuel Jackson, who is the Nick Fury of the Cinematic and Ultimate universes -and that's a discrepancy with Earth-616, whose Nick Fury doesn't look anything like that.
My best guess would be that after the end of Secret Wars (which hasn't been published yet) the universes get restored (or at least some of them do), but with some elements changed, one of which could be Fury.
Is there any official word about which universe the new Amazing Spider-Man takes part in?