So yes, the possessive in Korean is '내', '나의'. But when saying 'My favourite song' in Korea, the literal translation from Korean would be 'the song that I like the most', so it would be '내가 가장 좋아하는 노래'. A lot of the times when translating things into Korean, it's important not translate sentences literally. For example another sentence could be 'My song that I made' ----------'내 만든 노래', would be wrong. ----------'내가 만든 노래' - 'The song that I made' would be the correct way of saying it.