Cleopatra, also known as Cleopatra VII Philopator, was the last pharaoh of Ancient Egypt. She encounters Superboy on two separate occasions.
The first of these occurs in a 1961 chronicle when, at the Smallville High Athletic Fund Ball, the Boy of Steel while being approached by many of the girls in attendance, states that his ideal girl would be the late Queen Cleopatra. Also in attendance at the ball are Lana Lang and her uncle, the eccentric scientist Professor Phineas Potter who both overhear the hero's statement. Professor Potter, wanting to be of assistance to Superboy after hearing his statement, supposedly invents a cabinet-like time machine to bring the ancient queen out of the past and into Superboy's life in the present. However, this "Cleopatra" is not the real queen herself, but is in actuality the professor's niece Lana disguised in a black wig, who was attempting one of her many schemes to win the hero's heart, believing that Superboy will not be mad at her for tricking him.
This plan seems to backfire when Superboy lavishes extravagant gifts upon his queen. Lana, in a fit of rage, decides to treat the hero exactly as he treats her and act as if she can't be bothered with him. Stating to Superboy that she is bored and wants to go home to ancient Egypt, Lana is surprised when he wraps her in his indestructible cape and flies fast enough to break the time barrier and transports the two of them back to the ancient kingdom of the Nile. Arriving in the queen's palace, the two are momentarily placed under arrest by the real Cleopatra for the crime of royal impersonation until Superboy removes Lana's black wig and admits that he had known it was her in disguise the whole time. Superboy states that what led him to believe that it was a hoax was that the "so-called" time cabinet was made entirely of lead.
Before the two can return to their own time, Cleopatra's court magician, Ramses uses his magical abilities to prevent Superboy from leaving and captures them to be executed for the queen's amusement. However, before the execution can commence, Lana makes a last request that they play the "Bizarro Game", where everything must be said backwards. Ramses, agreeing to the terms of the game, is asked by Lana to speak his name backwards, and upon speaking the word "Sesmar", he disappears, restoring Superboy's powers. Lana had deduced that Ramses was a 5th-dimensional imp like Master Mxyzptlk and could be made to disappear if he were to speak his name backwards. Now freed, the two returned to the present time, with Cleopatra watching the Boy of Steel fly away and thinking that had she known he could fly, she would have fallen in love with him (Adv No. 291, Dec 1961: "Superboy's Romance with Cleopatra!")
The second of Superboy's encounters with the ancient queen occurs in an October 1969 chronicle, when the queen, now resurrected and disguised as a visiting student from modern Egypt named Cleop Amahdi hatches a complex plot to deceive the hero into believing that he has accidentally killed a fellow student at Smallville High, the aforementioned queen in disguise. Believing that he has broken his rule against the taking of life, Superboy sentences himself to eternal exile on a red sun planet, where his "powers will be lost forever." While leaving Earth, he briefly pauses on Earth's Moon. There, he spends much time in deliberation, first thinking, "Just exiling myself isn't enough! I--I'm guilty of destroying a human life!" However, he then begins to doubt that he has actually killed anyone and so returns to Earth to discover that Cleop couldn't have been killed by him because she had already been killed thousands of years ago by an asp in ancient Egypt (SB No. 160, Oct 1969: "I Chose Eternal Exile!").
(See also Cleopatra of the Potomac)