Hello James,
Welcome to E-T. - 3rd Class and Steerage were one and the same.
Looking at the 3rd Class List although the name is spelt differently might you mean: Johan Emil Petterson, who is listed as being on his way from: Västermo, Närlunda, Stora Sundby, Södermanland, Sweden to 4947 Lincoln Ave. Chicago. - It is noted that he was travelling with his sister: Johanna Ahlin.
In his book: Titanic The Great Lakes Connection, Cris Kohl, lists Pettersen, but not a John Paterson as: bound for Chicago.