The village is first mentioned in a document in 1427. Over the centuries, the name of the village gradually evolved from Baskócz recorded in 1773, through Baschkócz, Basskowce from 1786 to Baskócz, Basskowce from 1808. At the end of the 19th century, only the Hungarian the name Baskóc, which was later changed to Alsóbaskóc due to the difference from the village of the same name in the current district of Humenné. In the Hungarian geographical lexicon from 1851, the village is mentioned as mostly Russian (Ruthenian) with 228 inhabitants. Statistics from 1910 showed an increase in the population of Baškovce to 307.
After the First World War, the village fell to the Czech-Slovak Republic on the basis of the Trianon Peace Treaty. In the interwar period, only the Slovak name Baškovce was used. After the so-called The Baškovce fell to Horthy's Hungary during the small war between Slovakia and Hungary, but after the Second World War they were reunited to the Czechoslovak Republic.
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