They "arrived last evening in Bissau and turned themselves in to the (military) authorities," the source in Bissau told AFP.
The source, who asked not to be identified, did not explain how the fugitives had reached Guinea-Bissau, which is to the south of Gambia, but separated by Senegal.
A group of heavily armed men led by an army deserter attacked the presidential palace in the Gambian capital Banjul before dawn on Tuesday, but were repelled by forces loyal to Jammeh, who has ruled for 20 years.
Three suspects including the alleged ringleader identified as Lamin Sanneh were killed, according to a military officer.
According to a diplomatic source in Banjul, Jammeh appears to be preparing a purge of opponents, with "accusations flying".
"The names of military and civilian individuals are starting to be put on the table" at the feared National Intelligence Agency," the source said. "I'm afraid that innocent people are going to be caught up through denunciations.