Anime series/mangas like One Punch Man share many characteristics: they are about heroes, there is an association or group of heroes, there are heroes rankings, heroes have fandoms, their counteparts are villains and monsters, etc. These characteristics make them very similar between them, and though they might be categorized as "superpower", they are different to other shows where superpowers come from spiritual or magical sources such as Dragon Ball or Saint Seiya. Therefore I'd like to know, is there a specific anime category for shows like One Punch Man and My Hero Academia, which would make it easier to find others anime alike, or this is a new trend and there isnt?
I would have to agree with @AkiTanaka with this one. I think these anime can simply be classed as 'superhero' that is like a counterpart to Western superhero comics, like in DC or Marvel. What sets the 'superhero' genre apart is that there is a recurring theme of the 'good side', consisting of people referred by normal citizens as heroes or superheroes dedicated to fighting the 'bad side', consisting of what people would refer to as villains or monsters.
You might argue that since Gatchaman is categorized as superhero, this invalidates @AkiTanaka's point. If I understand correctly, Gatchaman characters do not have any powers comparable to that of Boku no Hero Academia or One Punch Man characters.
But, if you look at the definitions of what is a superhero, characters do not require actual superhuman powers or phenomena to be deemed superheroes. From Wikipedia,
...the longstanding Merriam-Webster dictionary gives the definition as "a fictional hero having extraordinary or superhuman powers; also: an exceptionally skillful or successful person"
Hence the reason why Gatchaman is also classed as 'superhero' and why I think BNHA and OPM can be classed as the same.