Barbara Gordon (younger)

The younger Barbara Gordon (b. 1993) is the daughter of Jim Gordon and her mother, the elder Barbara Gordon, as well as the sister of James Gordon.
Barbara first appeared when Jason Todd was being introduced to St. Philomena's Preparatory Academy, the school that she and his adoptive older brother, Dick Grayson, attended, and he would after as well, though he got into a fight at the time over Dick being called slurs by another student. A few years later, in April of 2003, she found out that the two's adoptive father, Bruce Wayne is Batman when Rachel Dawes abducted her family and took James hostage.
Over the next several years after that, Barbara looked forward to presenting, thinking that she was going to be either a beta or an omega because of her parents' genetics. However, as it turns out, due to a flip of her Θ gene, which would've led to her being an omega, Barbara is an alpha instead. Although she struggled with this initially, the revelation gave her the desire to become a vigilante herself after Jason got hurt as Robin. Initially wanting to protect him, she then decided to become Batgirl, albeit her reasonings eventually extended to simply wanting to do it for herself, too.
Her first time out as Batgirl, Barbara met Jason as Robin. The next day, when they met up at school, Jason realized that not only was Barbara Batgirl because of her scent, but that they were also scent matches because of it.