I studied . . . . . . . . modern history at . . . . . . . . university. In . . . . . . . . last year I specialized in . . . . . . . . history of . . . . . . . . Turkish Independence War.

The first blank won't take any article as 'modern history' is the name of a discipline. The second, third, fourth and fifth blank shall take 'the' as the sentence talks about a specific time's (history) particular event (Turkish Independence War) which was studied by the speaker at a particular place (university) in a particular year (last year).