The device appears to be a "stun gun" (not very helpful I know). Free lance artist Bartol Rendulić posted some concept art of the weapons online. I can't actually find any direct proof that Bartol did indeed work on X-Men: Apocalypse but the weapon in question does match the concept art posted by Bartol (that's not direct evidence in itself as it could have been drawn afterwards).
However, compare the device shown in the film and the concept art below.
Click images to enlarge.
If this is indeed actual concept art for the film there is also a small discrepancy with it, in that the concept art shows it being used to fire stun disks rather than shooting a sonic pulse of sorts.
Click image to enlarge.
It's also worth checking out the link with the full concept art as it gives designs for a smaller model and a handheld pistol version that fires darts.
I can't find any comic inspiration for the device and can't source what is mentioned in this answer so it may have been designed solely for the film.