Yozakura Quartet, Toaru Majutsu no Index Gaiden: Toaru Kagaku no Railgun Recommendations
A premise based on characters with special abilities. Yozakura Quartet and Railgun are about characters with superhuman powers beyond normalcy. There's a slice of life feeling on some cases but also story development involving our characters as revelations are unraveled.
The main female character is tough and independent. She is also dedicated with her duties and loyal to her friends. And on a more technical note, both series' action features clash of super powers.