score:4
I can think of one example. Tamar, the mighty Queen of Kings of Georgia (c. 1160-1213) married as her 2nd Husband David Soslan from Alania (who later sources claimed was also a member of the Bagrationi dynasty, her father's 4th cousin).
Their children included a son named George (1191-1223) and a daughter named Rusudan (c. 1194-1245).
George became King of Kings George IV of Georgia from 1213-1223. He died young and had a young son named David (1215-1270).
George's sister Rusudan became Queen of Kings in 1223. She married Ghis ad-Din, a member of the Muslim Seljuk dynasty. Their Children were David (1225-1293) and Tamar (d. 1286). Fearing that her nephew David would claim the throne, Rusudan had him imprisoned at the court of her son-in-law, Sultan KayKhusraw II, husband of Tamar. Rusudan sent her son David to the court of her overlord the Mongol Great Khan of Khans to be apointed ruler of Georgia. Tamar died while David was away.
David, son of George, was set free in 1242. In 1246 the Georgian nobles, believing that David son of Rusudan had died in 1244, selected David son of George, as the new king of kings, David VII Ulu. David VII Ulu was sent to the court of the Great Khan of Kans for official recognition, and was held there for five years, meeting his cousin David there. They were apointed to rule as joint monarchs. So David son of Rusudan became David VI Narin. And of course the relationships between the joint rulers and their descandants were complicated.
On the other hand, there are many examples in history when someone came to a place and claimed to be a monarch who had supposed died, and wanted to "reclaim" the throne. It seems like every time a monarch died tragically, or dramatically, or mysteriusly, or in a distant location, someone showed up claiming to be him or her.
Such claimants are almost always considered to be imposters by historians, and are usually described as the false person they claimed to be.
Here is a link to a list of false royal heritage claims.
https://en.wikipedia.org/wiki/List_of_impostors#False_royal_heritage_claims[1]
Of course that list is very incomplete.
Some more medieval examples of imposters are listed on page 36 of The Atheist’s Bible: The Most Dangerous Book That Never Existed, Georges Minois, 2012, is the statement that in the period 1300 to 1500:
Impostors were everywhere: A false Baldwin IX, a false Alfonso I, a false Fredrick II, a false Henry V, a false Conradin, a false Edward II, a false Richard II, a false Valdemar II, a false Warwick, a false York, a false Joan of Arc, false Popes, and even a false female Pope Joan.
I may add that there may have been two imposters claiming to be King Olaf (1370-1387) II of Denmark and IV of Norway, one in 1402 and one in 1387 or 88.
The one in 1402 is quite well known:
http://www.executedtoday.com/2008/09/28/1402-false-olaf-iv-michaelmas/[2]
The false Olaf from 1387 or 1388 is mentioned in The Middle Ages: Dictionary of World Biography, volume two, 1998, page 627:
“In Norway, a disaffected faction reported that Olaf was not dead. The Impostor claimed the crown and gained followers by revealing information that only Olaf or Margaret could know. Margaret hurried to Norway and proved that the impostor was the son of Olaf’s nurse by showing that he did not have large wart on his back Olaf’s birthmark. The false Olaf was tortured and burned at the stake.”
Upvote:1
Somewhat in line with the other answers, although with a happy end of sorts, is the story of the False Waldemar (der falsche Waldemar in German).
A case with a real monarch - albeit not with one assumed to be dead - would be that of the Zhengtong emperor of the Chinese Ming dynasty. He was captured by the Mongols and an successor was crowned. When the Mongols returned him some years later, he was imprisoned and only was able to return to the throne through some palace conspiracy.
Another more typical case is that of Thomas the Slav who apparently claimed to be the murdered Eastern Roman emperor Constantine VI.
Upvote:4
The various False Dmitriys who appeared during Russia's Time of Troubles following the death of Ivan the Terrible are probably the best-known examples.
The real Dmitry, Ivan the Terrible's youngest son, died (we think) in 1591 in his mother's retreat in Uglich. It is often assumed that Boris Godunov, who had ascended the throne when Dmitry's brother Feodor died, had the nine-year-old boy assassinated.
False Dmitry I may have been an illegitimate son of a Polish king, but he claimed to be Dmitry, spirited out of Uglich by his mother, who had anticipated Godunov's move. Godunov was extremely unpopular. Supported by Poland-Lithuania, "Dmitry" gathered an army, and in 1605 was poised to take Moscow and the throne when Godunov died. However, "Dmitry"'s reign only lasted a year. He was killed in 1606 when a mob stormed the Kremlin after a rumor spread by his eventual successor Vasily IV that "Dmitry" was going to make Russia convert to Roman Catholicism. (According to legend, his remains were stuffed into a cannon and fired west towards Poland.)
False Dmitry II appeared in Poland, where False Dmitri I's widow identified him as her dead husband. He gathered another army and was poised to take Moscow in 1610 when the Polish contingent of his army deserted him for their king Zygmunt III, who had decided to annex what Russian territory he could, and make his son Władysław the Tsar instead. (But not before he appointed Mikhail Romanov's father the Patriarch of Moscow). "Dmitry" fled to the Don Cossacks and conquered a lot of Southern Russia before a disgruntled officer got "Dmitry" drunk after a party, led him away and shot him.
(Meanwhile some boyars indicated they might support Władysław if he converted to Orthodoxy, but Zygmunt wasn't having that. The Polish occupation of Moscow ended in 1612).
But it wasn't over! Yet another impostor appeared in 1611, received support from the Cossacks again, and (based in Pskov) was proclaimed Tsar in 1612. But this didn't last long: He had to flee and was captured, taken to Moscow and killed. Whether by the Polish garrison or the Russians besieging them is unlcear.
This may be the end of it, or it may not. The linked Wikipedia article contains one of the funniest things I ever read in Wikipedia: "Some people argue that False Dmitry IV is just False Dmitry III due to bad record keeping". This might just be a joke someone edited into Wikipedia, however.
At the end, the 16-year-old son of the Patriarch raised by False Dmitry II was elected Tsar Michael, beginning the Romanov dynasty that (may have, kind of) lasted until 1918.
This happened during a few other Russian succession crises, such as when Pugachev led an insurrection against Catherine the Great, claiming to be her murdered husband Peter III. But False Dmitry I was the only one to actually sit on the throne.