Dorians

The Dorian invasion is part of the story the ancient Greeks told about themselves. Most of the people of the Peloponnese were thought to have been descendants of the Dorians, who were thought of as descendants of Hercules, the Heracleidae, from southern Macedonia, who settled the Peloponnese during the dark age of ancient Greece.

Here is one account of the Dorian invasion from the second century geographer Pausanias.

[4.3.3] After the conclusion of the Trojan war and the death of Nestor after his return home, the Dorian expedition and return of the Heracleidae, which took place two generations later, drove the descendants of Nestor from Messenia.
[4.3.6] The common people of the old Messenians were not dispossessed by the Dorians, but agreed to be ruled by Cresphontes and to divide the land with the Dorians.
Pausanias

Dark Age Migrations and the Dorian Invasion