Proton degeneracy generate what?

The degeneracy pressure of protons is the same pressure as that of neutrons and electrons. If the star's gravity is enough to defeat the degeneracy of electrons, it has defeated the similar electrostatic component of the proton leaving only the neutron degeneracy pressure of both neutrons and protons. Perhaps a better phrase for neutron degeneracy would be neutron and proton degeneracy pressure.

It is a good question

and John is wrong.

the problem of protons is that they are positively charged, and you will get a very large electric repulsion when you squeeze them together. This problem is obviously not present with neutrons...

Cheers!

See a more detailed explanation here:

http://www.phy.duke.edu/courses/055/faqs/faq20/

Is there such a thing as a proton degeneracy limit?

Well, since protons are fermions, degeneracy pressure can in principle apply to protons. However it's hardly ever a large effect, because you pretty much never have a situation where a bunch of protons (only) are squeezed into a small volume. The reason is that protons are positively charged, and you will get a very large electric repulsion when you squeeze them together.

In white dwarfs, the matter is made of atoms, which do have protons as well as electrons in them. However overall the matter is neutral, so the electric repulsion pressure is nullified. The degeneracy pressure is dominated by that of the electrons rather than that of the protons, since protons are more massive than electrons, and have less degeneracy pressure (see above question). For the case of neutron stars, there's also no electric repulsion pressure because neutrons are neutral, and it's neutron degeneracy pressure that matters.