。
Just who do you think I am?
Literal
Me [object-を] who [is-だ] [quotative-と] thinking-[state-ている] [explanation-の]?
A challenging/defensive rhetorical question. The pattern [A-を B-だと思う] ('think of A as B') is central: 僕を誰だと思う = 'think of me as who?' The ている + の ending gives it a demanding, incredulous feel — 'just who do you take me for?'. Typically uttered when offended, insulted, or challenged.