The Book of Daniel Is in Babylon During the Sixth Century BC

Daniel is in Babylon during the sixth century from basically roughly 598 BC to the end of his life. Daniel chapter one says that in the third year of the reign of Jehoa Kim, King of Judah, came Nebuchadnezzar, King of Babylon unto Jerusalem and besieged it. The statement right there in the very beginning of the book is off by seven years. So what do we know from this? This probably came later and it probably came at a time when the person writing down the story maybe didn't have access to all the information.