Is there historical proof outside the Bible of specific disciples of Jesus?

(I'm going to use CE for years in this answer, because while I don't like the CE system, AD might make readers think this it's the number of years after Jesus's birth, which it almost certainly isn't.)

Not exactly a disciple, but the historian Josephus talked about Jesus's brother, James, and also John the Baptist.

Josephus was an aristocratic Jew who rebelled against the Romans, was defeated, then became a slave of the Roman general Vespasian. He declared that God had told him that he'd sent Vespasian to punish the Jews, so other Jews believed he was essentially a self-serving traitor. When Vespasian became Emperor (69CE), he freed Josephus. Josephus became an advisor to Vespasian's son Titus, serving him as an interpreter in Titus's war against Jewish rebels (which led to the destruction of the Temple of Jerusalem). So Josephus, while a Jew, seems to have become loyal to the Romans.

After the war, he wrote four books for a Roman and Greek audience; The Jewish War (about 75CE), The Antiquities of the Jews (about 94CE), Against Apion, and the Life of Josephus Flavius.

Our particular interest here is a passage in The Antiquities of the Jews, which recounts an episode from when Josephus was a young man (probably 25).

"And now Caesar, upon hearing the death of Festus, sent Albinus into Judea, as procurator. But the king deprived Joseph of the high priesthood, and bestowed the succession to that dignity on the son of Ananus, who was also himself called Ananus. Now the report goes that this eldest Ananus proved a most fortunate man; for he had five sons who had all performed the office of a high priest to God, and who had himself enjoyed that dignity a long time formerly, which had never happened to any other of our high priests. But this younger Ananus, who, as we have told you already, took the high priesthood, was a bold man in his temper, and very insolent; he was also of the sect of the Sadducees, who are very rigid in judging offenders, above all the rest of the Jews, as we have already observed; when, therefore, Ananus was of this disposition, he thought he had now a proper opportunity [to exercise his authority]. Festus was now dead, and Albinus was but upon the road; so he assembled the sanhedrim of judges, and brought before them the brother of Jesus, who was called Christ, whose name was James, and some others, [or, some of his companions]; and when he had formed an accusation against them as breakers of the law, he delivered them to be stoned: but as for those who seemed the most equitable of the citizens, and such as were the most uneasy at the breach of the laws, they disliked what was done; they also sent to the king [Agrippa], desiring him to send to Ananus that he should act so no more, for that what he had already done was not to be justified; nay, some of them went also to meet Albinus, as he was upon his journey from Alexandria, and informed him that it was not lawful for Ananus to assemble a sanhedrim without his consent. Whereupon Albinus complied with what they said, and wrote in anger to Ananus, and threatened that he would bring him to punishment for what he had done; on which king Agrippa took the high priesthood from him, when he had ruled but three months, and made Jesus, the son of Damneus, high priest. "

It's very unlikely that Josephus saw this himself, of course. But he was from Jerusalem, and from an aristocratic priestly family, so it's more likely than not that, while his account may be biased in some way (in Josephus's earlier book he presents Albinus in a much nicer light), the general events are probably true. (The only other source we have for these events is a late 3rd century Christian historian quoting a 2nd century Christian writer, and as it focuses on James's holiness rather than the politics of the High Priests, it doesn't really contradict or agree with Josephus's account besides agreeing that it was by stoning, and happened in the 60s CE).

I should also say, as you asked about people who saw the resurrection of Jesus, that Paul in his writings claimed James had seen the resurrected Christ. In fact, according to the Bible, James did not actually believe his brother was the Messiah until after he saw Jesus after Jesus' death.
But we probably have no extant writings from James himself (there are writings in the Bible by a James, but James was a common name, and the writer doesn't mention that Jesus was his brother).

So, all we can say is that non-biblical sources confirm the Bible's depiction that Jesus's brother James was leader of the Christians in Jerusalem, and that some early Christians believed that James claimed to have seen the risen Jesus, just like they believed that some of their other leaders had (who probably did exist, because generally when sects claim their mortal leader is X, it is indeed X, but there's not actually any non-Christian sources from the first century still in existence that give names to any Christian leaders besides James and Jesus).

Of course, I can't say that James did claim to have seen his brother resurrected, only that some Christians believed he had. (It seems to me most likely that he did claim that, because Paul appears to have not really gotten along with James as they disagreed on theological matters, so I don't see a reason for Paul to give James the authority of having seen Jesus post-death, unless James himself claimed to have done so. But of course, I can't say for sure; our surviving sources on the beginning of a small and marginal religion 2000 years ago are not, unfortunately, very wide!)

Now, onto John the Baptist.

On John, Josephus wrote:"Now some of the Jews thought that the destruction of Herod's army* came from God, and that very justly, as a punishment of what he did against John, that was called the Baptist: for Herod slew him, who was a good man... Herod, who feared lest the great influence John had over the people might put it into his power and inclination to raise a rebellion... Accordingly he was sent a prisoner, out of Herod's suspicious temper, to Macherus, the castle I before mentioned, and was there put to death."

*This is a reference to King Aretas IV Philopatris, Herod Antipas's father-in-law. Herod divorced his wife, Aretas' daughter, so he could marry his brother's wife. This caused Aretas to invade and defeat Herod's army.

Note that this isn't the same as the Bible's account. Both agree that John was executed after Herod's divorce, but according to the Bible, Herod's new step-daughter impressed him with dancing, and when he promised her a reward, demanded the head of John the Baptist, who'd criticised Herod's new marriage.

Tldr;

It's most likely that James, leader of a Jewish sect's Jerusalem branch who venerated James's brother Jesus as the Messiah, was stoned to death in the 60s CE by the High Priest for some kind of offence against Jewish religious law (most likely connected to the fact he probably claimed his brother had been the Messiah).

It's also very likely that John the Baptist was executed in about 28 or 29 CE, as Herod saw his preaching as a threat.