What kind of punishment does Pip expect for striking the young gentleman in Great Expectations?

To answer this question, I think that you should look at
the first few paragraphs at the start of Chapter XII.  There, you can see Pip having
these sort of fevered fantasies about what will happen to him because he has beat up the
young gentleman.  I would say, overall, that Pip does not expect some particular
punishment.  Instead, it is clear that he just expects to be punished in some fairly
serious way.

If you need to give specific examples, look at
the paragraphs I've mentioned.  He imagines everything from him being put in jail to
kids being paid to beat him up to Miss Havisham herself shooting him.  So he has all
sorts of wild imaginings as to what punishment he might incur for what he has
done.