[j] is a convention meaning “the letter J” as opposed to /j/ “the sound of the letter Y in ‘yes.’” There is a [j] in Beijing: it’s the fourth letter in. There is no /j/ sound, neither in Chinese nor in any English pronunciation of it.
ETA: Of course there’s no [j] in Chinese full stop, only in the standard romanization of Chinese words. In that sense, both Beijing and Peking are attempts to render 北京 (pinyin běijīng).