This is another of the topics that I seem to write about once a week or even more often.
All fisheye lenses--all of them--produce a circular image that provides a 180-degree field of view. Why is that true? Because that's the definition of a fisheye.
To meet that requirement, the focal length of a lens with fisheye projection comes to around one-third of the diameter of the image circle when focused on infinity. Thus, if you want an image circle that is 15mm in diameter (so the whole image fits within the frame), you need a fisheye with a focal length of about 5mm. Sigma sells one.
If you want a fisheye image that the frame just fits within, so that you have (nearly) the 180-degree coverage corner to corner, you need one with a focal length of about 10mm for an APS-C sensor. Sigma sells one of those, too.
Tokina also sells a fisheye zoom that ranges from 10mm to 17mm, which is about the focal length needed to just accommodate the 24x36 format corner to corner.
So, you can buy an 8mm Peleng, and it will make an image circle 24mm in diameter. That will just fit within the 24x36 frame, making it a circular fisheye. On an APS-C sensor, that same lens won't quite reach to the corners of the sensor, so you end up with black corners.
One essential byproduct of providing a 180-degree field of view over the image circle is significant barrel distortion. It's not really distortion, because it is intentional. It is really fisheye projection. In that projection, no attempt is made to keep straight lines straight, except those that go through the center of the frame. Everything will look like it is reflected off a polished mirrored sphere.
Rectilinear lenses provide increase magnification in the corners sufficient to keep straight lines straight. They are actually harder to design than fisheye lenses. No rectillinear lens can approach 180-degree field of view.
Rick "if it doesn't say 'fisheye' it probably isn't one" Denney