A few Icelandic sagas tell about kings that ruled in Kvenland.
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Icelandic sagas
In Egils saga Faravid is directly said to be the "King of Kvenland".
Two other sagas that mention Kvenland, Hversu Noregr byggðist and Orkneyinga saga, do not use that specific title.
In Orkneyinga saga, Fornjót is said to be "a king". It is stated that he "reigned over Gotland, which we now know as Finland and Kvenland". The specific term "King of Kvenland" is not used.
Hversu Noregr byggðist has very similar usage for the title. This time, the great-grandson of Fornjót (who is said to be "a man"), Snær, and his son Thorri are told to be kings. Kvenland now appears in relation to Thorri, of whom it is said that "he ruled over Gothland, Kvenland (Kænlandi), and Finland". Fornjót's great-grandson Snær is also mentioned in Ynglingasaga, in relation to Finland.
In addition to Orkneyinga Saga (c. 1230), Hversu Noregr byggðist (c. 1387), and its appended Ættartölur (1387), medieval accounts that discuss the lineages sprung from Fornjót and his descendants - mainly Nór and Gór - leading to the later rulers of Sweden and other countries, include: Beowulf (8th-10th century), Íslendingabók (8th-10th century), Ynglingatal (late 9th century), Historia Norvegiæ (late 12th century), Skáldskaparmál (c. 1220), Hyndluljóð (13th century), Gesta Danorum (started c. 1185, finished c. 1216), Ynglinga saga (c. 1225), . However, whether or not Fornjót and his immediate descendants were actual historical people has been debated. Kyösti Julku notes that no geographical errors have been found in the descriptions of the Orkneyinga saga. He asks why therefore the people described in the account should be considered not to have existed.
Charles IX of Sweden
As a name for a country, Kvenland seems to have gone out of ordinary usage around the end the Viking Age. As the first ever account written in Swedish, Eric's Chronicle, was published as late as the 14th century, no medieval references to "Kvenland" or the "Kvens" are available from Swedish literature while Norwegian sources already mention the Kvens in the 13th century. However, King Charles IX of Sweden called himself ruler, among other peoples, of the "Caijaners". The king expanded his already lengthy title in 1607 CE to be as follows:
Carl then nijonde, Sweriges, Göthes, Wendes, finnars, carelers, lappers i nordlanden, the caijaners och esters i Lifland, etc. Konung [Charles IX, King of the Swedes, Goths, Wends, Finns, Karelians, Lapps in the Northland, the Caijanians and Estonians in Livonia, etc.]Julku and others have argued that "Caijaners", a Swedish name for the inhabitants of Kainuu, is here equivalent to the Old Norse kvenir, and some have seen an etymological link between Kven, Caijaner, and the Finnic term kainulainen/kainuulainen. Charles IX's claim can thus be seen as "king of the Kvens",
Charles IX's son dropped the term "Lappers j Nordlanden, the Caijaners" from the title in 1611 CE, when he succeeded his father as king, and it was not readded.