The first written mention of the village is preserved from 1247. In this document, the village is mentioned as "Bosk", the property of Pouša from the Abovce family, but it was established earlier. It was founded by four German and four Slovak families. This is evidenced by the original surnames of the first inhabitants of the village (Németh), as well as the names of localities in the village (eg "Bangord").
In 1322, Baška was owned by Dominik and Ján, sons of Matúš, son of Pouša from Baška. The mentioned owners of Baška probably came to the ownership in the times of feudal anarchy, when the Arpad family died out.
In 1427, the village belonged to Frank of Šemš and had 10 ports (Porta is the term for the gate that led to the road, with the estate behind the gate, ie a complete farmyard with several houses and purpose-built buildings.). In 1447, it became the property of the city of Košice, which bought Baška into its feudal property from the original owner, the local peasant and captain of Spiš Castle Petr. According to the Myslavic substitution from 1580, Baška thus became a part of the timber-mining business background of Košice.
Due to the relatively unfavorable terrain conditions, Baška was only weakly populated in the Middle Ages. In 1559 16 families lived here, in 1715 it had 2 households, in 1828 it had 27 houses and 198 inhabitants, in 1869 188 inhabitants lived here. Later, their number ranged between 200 and 300. At present, the village has 315 inhabitants.