There is a lot of archaeological evidence that supports the historical reliability of the Bible–especially the Old Testament. Here is a link to notes and a power point with dozens of such examples of evidence which proves the general reliability of the Old Testament. History Archaeology and the Bible Notes History Archaeology and the Bible PPT You will see that the evidence proves that David was a king and the first of a long line of kings of Judah. You will see evidence that supports the historical accuracy of Genesis, that supports the conquest under Joshua, Daniel’s account of the conquest of Babylon, and much, much more.
Because the kings of Israel and Judah were players in the wider world, we have several examples of archaeological evidence for the reality of Jehu, Jehoshaphat, Omri, Jehoiachin, Hezekiah and more. Please look at those in the notes and power point I provided above. But, what we do not have much of is discoveries that demonstrate the specific ministries of the prophets. The prophets of Israel were very significant to the Israelites, but to foreigners they were not all that important. For this reason we have almost no direct evidence to prove the existence of Isaiah, Elijah, Ezekiel and other prophets. Although we have archaeological evidence that supports historical events found in the books of Daniel and Jeremiah, we do not have mention of these prophets in non-Jewish sources. Of course, we have excellent evidence for all of these prophets from the most reliable source of ancient history, which is the Bible!!! But that is not what you are asking for.
The only direct evidence in archaeology that relates to the prophets is the discovery of a scarab of Baruch, the secretary of Jeremiah. In 1975 a collection of 250 clay seals (scarabs) were found about 44 miles southwest of Jerusalem. These seals were used to authenticate letters from their senders. One of them was from “Berekhyahu, son of Neriyahu the scribe.” This is almost certainly the Baruch of Jeremiah. Yahu was a common ending of names of Jewish people at the time. Baruch means blessed. Berekhyahu means blessed of God. The secretary of Jeremiah was Baruch, son of Neriah (Jeremiah 36:8). I am sure there was more than one Baruch, but given that the seal mentions a secretary Baruch, son of Neriah, and since it comes from about the right time, we can conclude that almost certainly this is the actual seal of the actual secretary of Jeremiah. If we can establish beyond reasonable doubt that the Baruch of Jeremiah is a real person in the position we know he had in the book of Jeremiah, then we can conclude that, almost certainly, the biblical prophet Jeremiah was a real person as well.
Of course, given the fantastically strong evidence that supports the reliability of the Old Testament in general, and given the clear belief of the Jews that Jeremiah was a real person, I believe that no reasonable person would doubt the reality of Jeremiah even without this evidence, but this is one example of what you are asking for, which is archaeological evidence for the Old Testament prophets.
BTW, I used the website http://www.biblehistory.net/newsletter/baruch_jeremiah.htm for some of this information.
Here is an image of the relevant seal.