Mytheline is probably a misspelling of Mytilene, a port city in the island of Lesbos. In Ottoman times it was referred as 'Midili'. During the late fifteenth century, the Barbarossa brothers established a privateering base there against the Knights of St. John. Later on, Lesbos was transformed into a sancak (subprovince) under the province of Aegean Islands (Cezayir-i Bahr-i Sefid)

According to the texts. those were "Adventurers under a Sanjaz-Bey". These men would probably be auxiliaries or levends (marines of Ottoman pirate ships) recruited by the sancak bey, who obliged to join military expeditions on their own squadron. At 1566, the squadron of Lesbos only contained two galleys for coast guarding, but the men manning the ships would've been used in a military campaign.

Sources:

"The Barbary Pirates" by Angus Konstam

"The Ottoman Empire 1300-1650" by Colin Imber