"나 잠시만 뭐 사가지고 올께" => I'll go get[buy] something really quickly.
- 나: I - the subject. The topic/subject marker 은/는, 이/가 may follow the subject but not always, as in here.
- 잠시만: 잠시(a moment, a short while) + 만(only) => just for a while, briefly.
- 뭐: contraction of 무엇 (what, something). The object marker 를 is omitted.
- 사가지고: 사(buy) + 가지고(with something; carrying something) => "buy and ...".
- 올게: 오다(come) + ~ㄹ게(sentence ending expressing an intention). "-ㄹ꼐" is a nonstandard spelling.
Grammatically, you may think of it as 나는 잠시만 무엇을 사(서) 가지고 올게.
But this is how it is said most of the time.