This is a tough question to answer, but remember that it also is a subjective question. Not all readers are going to agree on which character is the most influential person in Steve's life. Part of the difficulty of this question is that readers do not get much insight into many of the potentially influential people in Steve's life. A person could argue that men like King are the most influential. That makes sense, since Steve is in his situation because he spent time around those guys and admired them in some way, but I'd like to think that Steve has more positive influencers in his life.
Steve's mom is a good choice. Readers see throughout the story that Steve has a good heart. He isn't like the rest of the men in jail. He fears he is a monster, and that helps convince us that he isn't a monster. He doesn't want to be that kind of person, and Steve's parents are a big reason for that. His mother never stops believing in his innocence, and that shows her unconditional love. This is helpful for Steve's overall mental and emotional health. Unfortunately, Steve's mother struggles with giving him this kind of support once he's in jail. She can't bring herself to visit that much.
A big clue for answering this question can be found in the list that O'Brien makes Steve write down. She makes him write down the names of the people that he admires. His teacher Mr. Sawicki makes the list. Mr. Sawicki is a film teacher, and he teaches Steve a lot about the process. It turns out that Mr. Sawicki's teachings are what allow Steve to cope with what is happening around him in the court and the jail. Mr. Sawicki is also called into the court proceedings as a character witness, and he speaks very positively about Steve. This breathes life into Steve and gives him hope in addition to influencing the future outcome of the trial itself.