There is evidence they did, and she had his son, named Caesarion (Little Caesar) in 47 BCE. Julius Caesar never officially acknowledged Caersarion as his son, but he let the boy use his name. Caesarion was also said to have the looks of Caesar. However, there is some classical political writings claiming Caesar could not have been the father. After Caesar was assassinated in 44 BCE, Caesarion and Cleopatra went back to Egypt, where he helped to rule as King of Kings, until Octavian (Caesar's adopted son) had him killed in 30 BCE, again for political reasons.

It's highly likely that the relationship between Cleopatra and Julius Caesar was strictly for political gain. It began around the time Caesar sided with Cleopatra against her brother Ptolemy XIV in her fight for the throne.