The four guys come in with immediate and pretty strong hostility. The one who is supposed to be Pavlichev's son can't put two words together, so Ippolit mostly does the talking for him.
Myshkin offers them a chance to chat in another room, and is generally surprised that they are there at all since he asked Ganya to deal with this whole situation.
After some arguing, and when they can't come to their point, Mrs. Epanchin asks Kolya to read an article in the paper—Lebedev has just handed it to her.
The article is basically a long exposition about who these guys are and what they want—which really is a pretty good way of laying out the basic plot so the characters can go back to fighting. Good plan, Dostoevsky.
So, yeah. In the article, which is written as insultingly and nastily as possible, the basic allegation is that Pavlichev, the man who raised Myshkin and who sent him abroad to Switzerland for treatment, also had an illegitimate son whom he totally forgot about and never spent any money on. There is lots of slander about how Myshkin is basically a non-functioning idiot, and how Pavlichev was a gross old lecher. Then the article demands that Myshkin pay this illegitimate son back all the money that Pavlichev spent on his education and treatment—since, as a son, he is the one who should have gotten all that money in the first place. Which, um, okay, we guess there's a kind of logic there, but honestly, if you are asking someone for something, a word of a advice is not to first insult them head to toe. You know, just in case.
When Kolya is done reading, everyone is totally mortified.
The prince is all, why on earth would you publish this crazy thing?
It turns out that the one who wrote it is the ex-military guy, and the other three renounce the article.
But this is neither here nor there, says Ippolit, screaming that they are there to get the money, and if the prince has any honor then he will repay the debt.
The prince is all, okay, here is ten grand.
But then he goes on to say that after Antip's lawyer first contacted him, he could tell that this greasy lawyer was clearly the instigator—and now, seeing that Antip is barely verbal, Myshkin wonders whether or not he might also be an epileptic? And then, even if not, Myshkin says that Antip is clearly a simple, easily deluded man, who has been tricked into starting this whole scandal by this lawyer.
Why does he know all of this?
Well, because Ganya has been investigating, and Antip is totally not Pavlichev's son. Whoah.