The first case, 내 is contraction of "나의" 제 is contraction of "저의" 의 is a possessive particle similar to 's. Ex) 나의 책 = 저의 책 = 내 책 = 제 책 = my book Use 내 and 제 before a noun The second case, 나 and 저 are changed into 내 and 제 before subject particle 가. 나 + 가 => 내가 저 + 가 => 제가 내가 말했다 = 제가 말했어요 = I said that 나가 말했다(X) 저가 말했다(X) cf. 나는 말했다 = 저는 말했어요 = I said that

나 is informal and is usually used with 반말 but can be used with the 요 form too. 저 is a humble (and more polite) form of "I" and is used with the 요 and ㅂ니다 forms. Likewise, given that 내 and 제 are simply contractions using those two, the same rules apply (내 is informal, 제 is humble aka more polite).