On

On is used to indicate or show (1) the position in contact with and supported by the top surface of: ‘The book is lying on the table.’ (2) a source of attachment or support: ‘Hang your shirt on that hook.’ ‘Clock on the wall’ (3) a means of transport or conveyance: ‘I came to office on my bike.’ (4) a day or date or timeframe during which something takes place: ‘I will meet you sometime on Tuesday.’ (5) about something/somebody; on the topic of : ‘He wrote a book on History.’ (6) the location of something: ‘There is a coconut tree on the left side of our house.’ (7) continuity, persistence or concentration: ‘Shall I read on?’

You see a report, advertisement, photograph, etc in a newspaper or magazine (NOT on): ‘I came across the article in this month’s edition of Woman’s World.’