Both are correct. 내 is casual and 저의 is formal. 나 is the casual version of I 저 is the formal version of I When you want to say 'my' you add 의 to end 나의 저의 but often words in Korean are made shorter for ease of pronunciation. 나의 becomes 내 저의 becomes 제 It's more common to see '내' than '나의'

Thanks a lot sujin kim :)