They were arrested in Kanilai, Jammeh's home village, which is situated more than a hundred kilometres from the capital city Banjul.
The spokesperson for the Gambia police force, Inspector Foday Conta, confirmed the arrests to APA, and identified the men as Jalamang Jammeh, Sainey Jammeh and Adama Jammeh.
Conta said they were rounded up on Wednesday, but did not disclose the reason for their arrest.
This reported arrest of people who were close to former president Jammeh, comes just a month after three Gambian soldiers were shot in the leg by ECOMIG troops, which the Gambian authorities described as ''accidental'' firing in an incident which also reportedly happened in Kanilai.
Jammeh was forced to leave the country in January 2017 for exile in Equatorial Guinea, after ECOMIG troops were deployed in The Gambia by ECOWAS.
The new government of President Adama Barrow has been actively investigating atrocities allegedly committed by Jammeh, and presently nine persons, among them one Yankuba Badjie, the head of the former national intelligence agency under Jammeh’s government, are on trial at the high court in Banjul charged with various crimes, including the murder of former opposition youth leader Solo Sandeng.