Characters don't have genres. Fiction has genres -- see the link below for some of them.
Genre can be recognized by terminology and character archetypes. Additionally, tone and figures of speech can be good indicators of genre.
Satire or irony
he talks from the main character
morality play
In the horror genre, the final girl character type is common. This character is typically a young woman who is resourceful, smart, and ultimately survives the horrors that the story presents, often being the last one standing against the villain or antagonist.
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A book focused on character development would likely be classified as literary fiction or a character-driven novel. This genre emphasizes the internal growth and change of the characters and their relationships more than external plot events.
Poe was credited for creating the genre of detective fiction with his story "The Murders in the Rue Morgue," featuring the character C. Auguste Dupin.
The genre of superhero fiction is most likely to use a superhuman character as a hero or protagonist. This genre focuses on characters with exceptional abilities who battle evil and protect society from threats using their extraordinary powers.
"The Old Man in the Park" is a short story that falls under the genre of fiction. It can also be categorized as a character-driven narrative due to its focus on the old man and his experiences.