Fem!Harry, best known as Jamie, Harri, Rose, Lily (Jr?), or often just 'Harry' Potter, is a rare but interesting character within the Harry Potter fanfiction community. Her origins, of which she roughly has two, stem from the gender of her writer, and tend to influence what type of character she is.
When found as the main character, she is usually just a female stand-in for canon Harry, and goes on to have several similar, very similar, or vastly different adventures, spanning from being a love interest for a variety of Slytherin males, plus Snape, to being an Amazonian elemental princess that insists on being naked. Typically known under the 'Rose' alias, she is usually a carbon copy of her mother - red haired and green eyed. Her existence can be summarized by the effect of '90s feminism on an entire generation of girls.
A notable exception to the typical Mary-Sue sterotypes of the stand-in Fem!Harry is SlyGoddess' popular A Butterfly Effect. It exploded onto the scene in the summer of 2010, retelling the familiar tale in new, intricate, and exciting ways. Given the author's sexual preferences, Harriet aka 'Harry' is an intriguing blend of both male and female archetypes. Based upon the personality traits that HJP shares with victims of abuse-derived Covert Schizoid Personality Disorder, the Fem!Harry is contrarily portrayed as having a textbook case of Overt Schizoid PD. As the title implies, this small yet essential variation in character gradually builds exponential change, resulting in entirely different outcomes. While this story is not yet complete, it is a shining beacon of hope for supporters of the stand-in Fem!Harry subgenre and has spawned a veriable flurry of spinoffs.
Her other, vastly more interesting origin is as an inhabitant of another universe, where Harry himself visits. This is, of course, the inescapable setup for the infamous Harry/Fem!Harry pairing. The concept was pioneered in 2005 with SilverAegis' unfinished story Harry Potter and the Girl Who Lived. Numerous attempts to finish it have all failed with few, notable, exceptions. All of these SilverAegis derivatives feature a fourteen year old 'Lily', who, like the 'Rose' persona above, is red haired and green eyed.
A second attempt at the alternate universe female Harry was made in Amerision's Equal and Opposite. This version features 'Jamie', who looks more in-line with a 'Fem!Harry', featuring black hair and green eyes. Unlike 'Rose', 'Jamie' is a polar opposite of Harry in terms of personality, harboring sociopathic traits and a penchant for evil.