A Certain Magical Index

Set in a city of scientifically advanced superhuman students, but in a world where magic is also real. Touma Kamijou’s right hand, the Imagine Breaker, will negate all magic, psychic, or divine powers, but not his own bad luck. One day he finds a young girl hanging on his balcony railing. She turns out to be a nun from the Church of England, and her mind has been implanted with the Index-Librorum-Prohibitorum - all the magical texts the Church has removed from circulation.

A Certain Scientific Railgun S

The second season of Toaru Kagaku no Railgun</i>. Something sinister is going on in Academy City. The shadows are filled with whispers of an organization cloning super-powered students known as espers. High-ranking master of electricity, Mikoto Misaka, laughs off these stories until she comes face to face with a copy of herself. After learning that these clones - her sisters - are being systematically murdered in a series of experiments designed to turn a sadistic killer into the strongest esper in history, Misaka vows to save her copies and destroy the organization responsible for the project. As Misaka prepares to face off against the organization’s power-hungry esper, she discovers that she wasn’t the only victim of the scientific forces conspiring within the city - and that’s something Misaka and the girls of Judgement simply won’t stand for. (Source: Funimation)

A Certain Scientific Accelerator

The espers of Academy City are classified into six levels, where "Level 0" lacks power while "Level 5" possesses an overwhelming amount. Of the several million espers residing in Academy City, only seven of them have attained Level 5, and ranked highest among them is the one known as Accelerator. Toaru Kagaku no Accelerator focuses on the strongest Level 5 after he protects the cheerful Last Order at the price of much of his power. Recovering at the hospital, Accelerator has led a relatively quiet life until he ends up saving the life of Estelle Rosenthal, a mysterious girl carrying a photo of Last Order. Unfortunately, Accelerator now finds himself dragged into a new conflict in the form of a sinister organization called Disciplinary Action which plots to use Last Order for a dangerous mission. Now that they have set their plan into motion and are in pursuit of the young girl, it's up to the world's most powerful esper and his newfound companion to protect Last Order and defend Academy City in the process. (Source: MAL Rewrite)

A Certain Scientific Railgun

Academy City is a highly developed place in terms of technology. It is said to be 20 to 30 years ahead of the rest of the world, and 80% of its 2.3 million residents are students. The focus of studies here is directed towards esper powers. Misaka Mikoto, one of the top level espers in town, shares a room with Kuroko Shirai, another high level esper who is a member of Judgement, a law enforcing agency composed of students. Both attend Tokiwadai, a private school reserved for the high-leveled and the rich. Kuroko's partner at Judgement, Kazari Uiharu, is a low level esper who studies at Sakugawa middle school. Her best friend and classmate there is Ruiko Saten, a level zero, one who has no esper powers. Together, the four encounter several adventures in the exciting scientific town. (Source: Anime News Network)