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'