I once read this manga about esp and/or special abilities/powers. The main character was a boy. It starts off with him on his way to school(?) and he sees a baby fall from a balcony, (talk about irresponsible parenting), and he thinks he won't make it in time. Another girl pops out of nowhere and uses her power to save the child. Also, I think at this point he thinks he doesn't have any powers.
Extra stuff I remember:
-He has a famous older brother. (Amazing powers or something?) -He's also attending an special school, I think.