I also got the feeling Jimmy was Nucky's son, but I think Jimmy's son was Jimmy's son, because it was mentioned his girlfriend was already pregnant when he went to fight in the war. Only when he was away she cheated on him. His son only saw the man she cheated with in his first years and that's why he had an affection to that man, which Jimmy noticed and that's why he became aware that his girlfriend had cheated on him.