What kind of punishment does Pip expect for striking the young gentleman in Great Expectations?
With his hyper-imagination, Pip fears that he will be sent to jail, or beaten, even possibly killed by Miss Havisham for having fought and hurt the pale young gentleman.
Since one of the tropes of the novel is of society itself being a prison, Pip's imagination is besieged with images of chains, locks and bolts, and criminality. Such ideas have been fostered by his association with the convict at the graveyard, as well as his guilt over having stolen food and drink from his sister's pantry. Certainly, his excessive beatings from Tickler (Mrs. Joe's cane) for inconsequential things heightens his fear of punitive measures against him for any actions which are not proper.
Added to these already extant fears is Pip's new sense that the upper class is superior to him, and actions against them must, therefore, be considered criminal. After the exaggerated importance his sister and Uncle Pumblechook have placed upon his going to Miss Havisham's, and the cruel and derogatory remarks Estella has made with impunity, Pip can only believe that he truly is inferior to the pale young gentleman and will, therefore, be punished severely:
I felt that the pale young gentleman's blood was on my head, and that the Law would avenge it. Without having any definite idea of the penalties I had incurred, it was clear to me that village boys could not go stalking about the country, ravaging the houses of gentlefolks and pitching into the studious youth of England, without laying themselves open to severe punishment. (Chapter XII)
This unreasonable sense of the superiority of the aristocracy impairs Pip's thinking after his fight, and it blocks his reasoning in years to come, causing him to reject Joe and Magwitch because he considers them inferior to Estella and Miss Havisham, rejections that cost Pip real loving feelings.
After striking the pale young gentleman, Pip fully expects to be jailed. At the beginning of Chapter XII in Volume I, he says, "I felt that the pale young gentleman's blood was on my head, and that the Law would avenge it" (page 93). For several days after he fights with the pale young gentleman, Pip does not stray far from home, as he expects that officers of the County Jail will soon put him in prison. When he returns to Miss Havisham's house, he is afraid that policemen from London will be waiting to capture him, and he also fears that Miss Havisham will shoot him with a pistol. Finally, he believes that mercenaries will attack him in the brewery. However, nothing actually happens to Pip, even after he returns to Miss Havisham's house. In a strange twist of fate, Pip meets the pale young gentleman again in London several years later. He is Herbert Pocket, who becomes one of Pip's best friends.
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.