"Caesar's wife must be beyond suspicion" is a proverbial phrase which suggests that individuals in prominent positions or those associated with powerful figures must not be under any suspicion, even if that suspicion is groundless. The saying speaks to the idea that those closely associated with public figures must not only be virtuous, but also appear to be so in the eyes of the public.
The origin of the phrase traces back to a historical incident involving Julius Caesar. His wife, Pompeia, hosted the Bona Dea festival which was exclusively for women. However, a young patrician named Publius Clodius Pulcher disguised himself as a woman and sneaked into the event, allegedly to seduce Caesar's wife. He was caught, leading to a major scandal in Rome. Even though it wasn't proven that Pompeia had anything to do with him or was even aware of his intentions, Caesar decided to divorce her. When asked about his decision, Caesar reportedly said, "My wife ought not even to be under suspicion." This reflected his belief that members of his family should be above reproach, regardless of whether they were actually guilty.
The phrase has since been adopted to indicate that individuals in positions of responsibility or in the public eye (and those associated with them) should be above suspicion and avoid even the appearance of impropriety.