When asking about a subjective character, you might be referring to the "subjective character of experience," which is a psychology term coined by psychologist Thomas Nagel in his very influential paper titled "What is it Like to Be a Bat?" Through using the term, he argues that all conscious beings see their environment differently, and it is possible to speak of that beings own subjective view and experience of his/her own environment. All characters in Harper Lee's To Kill a Mockingbird see their environment subjectively, with the exception of Atticus, who always strives to see things from others' points of view. Eventually, other characters learn from Atticus about how to see from others' perspectives.
One good example of a character who only sees from a subjective view is Aunt Alexandra. Unlike her brother Atticus, Alexandra is very stuck in her ways. In particular, she has very old-school views about what society should value. She sees the Finches as very important members of society because they have a long history of being wealthy, educated landowners. As a result of her views, she attempts to get her brother to raise his children to believe their family is special. When she first moves into the Finch household to help Atticus raise his children, at her prompting, Atticus goes into Jem's room to make the following speech to his children:
Your aunt has asked me to try and impress upon you and Jean Louise that you are not from run-of-the-mill people, that you are the product of several generations' gentle breeding-- ... and that you should try to live up to your name-- (Ch. 13)
However, when Scout breaks down in tears, Atticus recants. He implies that he doesn't agree with his sister's view of what is important and tells his children to forget what he had said, to forget about the importance of behaving like a Finch.
Since Aunt Alexandra sees herself and the Finch family as very special, she looks down her nose at others, especially African Americans and farmers. She refuses to understand Atticus's desires to treat Calpurnia as one of the family and even to understand why he is defending Tom Robinson. In addition, when Scout says she wants to invite her schoolmate Walter Cunningham home for lunch once school starts up again, Aunt Alexandra refuses to permit it; she even stoops so low as to say, "[H]e--is--trash," which angers Scout to the point of tears and shows us that Aunt Alexandra is unable to see her environment from any perspective but her own (Ch. 23).