Monster, Yuureitou Recommendations
Both main characters are both on the run and trying to solve a crime they did not commit. As they both continue their journey of trying to solve the crime the stories become more in depth. Both mangas will have you sitting at the edge of your seat. There are definitely a lot of OMG moments in both mangas.
Both have protagonists on the run because they’ve been accused of crimes they did not commit. They are both psychological and engrossing with complex characters and expositions of the evils of humanity.