To answer this question, you must first identify the qualities of the mockingbird as they're given in the novel. When Jem gets an air-rifle for Christmas, Atticus explains to him that he may shoot as many bluejays as he wants but it's a sin to kill a mockingbird--the only time his father ever called any behavior a sin, Jem noted.
Miss Maudie goes on to explain: "Mockingbirds don't do a thing but make music for us to enjoy. They don't eat up people's gardens, don't nest in corncribs, they don't do one thing but sing their hearts out for us."
As applied to people, then, you must look for characters who are "targets" of people who want to "shoot" them, either literally or figuratively. Characters who are innocent and helpful, wanting nothing more than to help others, yet are in danger from others. That brings two characters to mind: Boo Radley and Tom Robinson.
Boo is the target of town gossip and children's pranks, yet the only three things we know for certain he does in the novel are acts of selflessness. Boo puts thoughtful gifts in a tree for the two kids, he puts a blanket around Scout as she watches Miss Maudie's house burn, and he saves Jem's life. The episode with Jem is even more dramatic, of course, because he actually kills Bob Ewell to save the young boy's life. Boo is the epitome of a mockingbird who wants nothing but to live a peaceful life and make music, so to speak, for others.
Tom Robinson is another character who is nothing but kind--even to those who eventually turn on him. Even though Tom helps Mayella out of kindness and pity, Mayella is trapped and must accuse him of accosting her to save her own life. Tom has done nothing wrong or improper, yet he is shot--in this case literally, many times--by a society which does not value the word or the life of a black man. He, too, is the embodiment of that innocent bird who wants only to live in peace and sing when he can.
While there may be others (perhaps Mayella, and even Ol' Tim Johnson, for example), these two characters most exemplify the qualities of a mockingbird in this novel.