not have anything on (someone or something)
1. To have no discernible advantage over someone or something else; to not be any better than someone or something. Yeah, you're pretty good at basketball, but you don't have anything on my older brother Steve. Video game systems have gotten pretty impressive in recent years, but in my opinion they don't have anything on the classic systems from the '90s.
2. To have no decisive incriminating evidence against someone; to have no proof of wrongdoing or criminality about someone. The police can insinuate all they want, but they know they don't have anything on me that'll stick.
3. To have no information available about someone or something. I got this history book for my report, but it actually doesn't have anything on the topic I want to write about! The library is horribly outdated—it doesn't even have anything on the current president!