The presence of Zakynthos is marked by mythical times.
The first reference to the island is made by Homer in his works Iliad and Odyssey. It is said that it got its name from Zakynthos, son of the king of Phrygia Dardanos. Zakynthos with Achaean warriors from the city of Psofida in Arcadia, where his brothers reigned, was the first to inhabit the island, giving it its name. He even built a citadel, probably on the spot where the Venetian castle is today, which he named Psofida.
According to the testimonies of Pausanias and Thucydides this happened in 1500 BC. The new inhabitants worshiped the Olympian gods, especially Apollo and Artemis, as evidenced by ancient coins that have been found on the island.
Zakynthos did not take part in the Persian wars. In the Peloponnesian War he supported the Athenian alliance and participated in the campaign against Sicily. After the failure of the campaign, the Athenian alliance was dissolved and Zakynthos was conquered by the Spartans. It would later be under Macedonian rule until it was finally conquered by the Roman Empire.

Source: Municipality of Zakynthos
http://www.zakynthos.gov.gr/