Superman: The 10 Cent Adventure
When a crazed villain named Radion attacks Metropolis, a young girl in a costume leaps into battle and throws the villain into a nuclear reactor (in front of a TV news crew and Lois Lane). The girl identifies herself as Supergirl, Superman's daughter. Upset, Lois confronts Superman, accusing him of having an affair, and refusing to believe his claim of innocence, since "Supergirl" looks just like him. However after a cup of the new "Yes" coffee, Lois suddenly calms down and dismisses "Supergirl" as a villain's hoax, until she lands in front of Lois and calls her "Mommy". Superman confronts the girl, who argues that she is his daughter with Lois, and that her name is "Cir-El". Cir-El says that she is from the future, brought to the past by the Futuresmiths. When Superman encounters the Futuresmiths, they show him a horrific future, with robotic monsters attacking civilians, and he sees himself as a cybernetic Superman attacking civilians as well. The Futuresmiths tell him that Cir-El's death will prevent this future, and as they turn to attack her, Superman flies her to safety. S.T.A.R. Labs confirms that she is his daughter, but that Lois is not her mother. Regardless of her identity, Superman comes to regard Cir-El as family.
Cir-El helps Superman fight off a diseased Bizarro. Later, she fights off with the aid of Natasha Irons and Girl 13, a vengeance-crazed superhuman ninja who is killing Superman. When Superman and Batman are said to be "captured" by President Lex Luthor in Superman/Batman "Public Enemies", Cir-El teams up with Superboy, Krypto, Natasha Irons, and the Batman Family to rescue them. Batman, not actually having been captured, is the one to save Cir-El and Superboy from a White House death trap.
Superman has a shock when, while talking to Cir-El, she changes into an angry young woman named Mia, who hates her Cir-El persona. Superman's Kryptonian robot Kelex subsequently confirms that Cir-El is not the Man of Steel's biological daughter (despite the evidence from S.T.A.R. Labs). While the girl's D.N.A. has some Kryptonian attributes, she is primarily human.
Disaster strikes when a future Superman appears and shows Superman a devastating future with Lois dying, Wonder Woman and Batman turned into cyborgs by a nano-tech virus concealed in "Yes" coffee, and Cir-El trapped in a giant Brainiac robot. Brainiac reveals that Cir-El is his "Trojan Horse", that he has concealed part of himself in the one thing he knows Superman would never harm: his 'child'. Cir-El was created by Brainiac by grafting some Kryptonian DNA onto the body of Mia. He then implanted false memories in Cir-El and had his servants, the Futuresmiths, send her out into the world (along with the nano-virus, which was placed in "Yes" coffee to proliferate the virus and infect the population) in order to unknowingly alter the future, and lead Superman to create a synthetic body to save Lois from her "Yes" infection in the future (for Brainiac to inhabit). Horrified, Cir-El throws herself into a time portal to prevent herself from being born, and thus, prevent the future from ever happening.
The return of Cir-El
Thanks to the time-traveling efforts of Bizarro in Superman/Batman #24, Cir-El is able to join Linda Danvers, Kara Zor-El (both Modern Age and Pre-Crisis versions) and Power Girl to rescue Superman from the Source Wall. The girls are successful, but Superman only recognizes Kara, Power Girl, and Linda, due to Cir-El and pre-Crisis Kara Zor-El coming from previously erased timelines.
Cir-El and the other Supergirls then assist Superman and Batman in a reality-altering fight against various menaces from many alternate dimensions. At the conclusion of the fight, Mister Mxyzptlk sent Cir-El and everyone else involved back to their appropriate locations.
Powers and abilities
A hybrid of human/Kryptonian origin, Cir-El absorbs yellow sunlight to gain superhuman strength and speed, super-hearing, and invulnerability. Originally, instead of flying, Cir-El could leap vast distances, although she is later seen flying in Superman/Batman #5, and again in issue 24. Her "trademark" power is the ability to release her stored solar energy from her hands as "Red Sunbursts", blasts of red solar radiation (the very wavelength of sunlight that Superman loses his powers under) that strike an enemy with intense heat and force. Like Superman, she is vulnerable to Kryptonite.
The only other human/Kryptonian hybrid, Superboy, inherited (eventually, through retcon) more traditional powers because his D.N.A. is 50 percent Kryptonian, whereas Cir-El's D.N.A. is primarily human, with some grafted-on Kryptonian attributes.