The reason Mr. Cruz was arrested, however, is less clear, and he has offered different explanations. In an interview alongside his son in March, Mr. Cruz said he had sought to recruit to the revolutionary cause someone who turned out to be an informant working for Batista’s regime. The 1959 account, though, did not mention any informant; Rafael Cruz said then that the authorities were alerted to his involvement in the resistance by another man, who gave up only Mr. Cruz’s name after Batista’s forces beat it out of him and left him bleeding in the same cell as Mr. Cruz.

Mario Martínez, who Mr. Cruz confirmed was part of his small revolutionary cell, said he did not recall Mr. Cruz’s being apprehended for trying to recruit someone and said he believed that the cause of his old comrade’s detainment was possession of a revolver — one that Mr. Cruz had never used.

Mr. Martínez declined to be directly interviewed and relayed answers to questions posed by The New York Times about Mr. Cruz through Ms. Arestuche. According to Mr. Martínez’s account, he and Mr. Cruz had belonged to the youth brigade of Mr. Castro’s 26th of July Movement in their hometown, Matanzas, but had done little besides join in protest marches. They never turned to violence, he said.

The fog of almost 60 years can cloud even the clearest of memories, and it is possible that witnesses who can back up Mr. Cruz’s account might exist and come forward. But none of the Cuban historians, former comrades of Mr. Cruz in his hometown or veterans of the Santiago battle reached by The Times could corroborate his story.

Approached in Marietta, Ohio, on Oct. 13, between wooing campaign donors and headlining a Republican dinner, Mr. Cruz was unable to provide the name of any participant from the Santiago assault. “I mean, we were scattered,” he said, adding, “I was with one other guy at a little coffee place or something like that, and I don’t remember his name.”

Unlike some other American presidential candidates, Ted Cruz remains largely unknown in Cuba, and most of the people interviewed for this article had never heard of him. But the Cruz campaign rejected those who disputed Rafael Cruz’s version of events as politically motivated.