I was watching some program today and somebody said '내 마우스에서 나왔드랬죠'. I'm wondering what the '드랬다'part of this means. Does it just have the same meaning as '다고 했다'? Thanks.
-드- is a non-standard alternative to -더-; speakers of some dialects pronounce ㅓ as 으. -았더랬죠 just means -았죠 or -았어요 there although -았더랬죠 is the contraction for -았더라고 하였죠 or -았더라고 했죠.
From a critical viewpoint, we can say that -았더랬죠 is logically wrong for your example because -았더라고 했죠 should be used to say what others said about their experience. "내 마우스" is the speaker's own mouse or mouth (마우스 meaning mouth is also a non-standard word), so she/he is talking about her/his own experience. Thus, your example sentence needs to be corrected as "내 마우스에서 나왔어요." (If 마우스 means mouth, "내 입에서 나왔어요.")
If we look at it from a different perspective, -았드랬- can be accepted as a dialect ending. According to a dictionary, -랬- is a dialect ending of a word used with -더- (which I think has to be -았드- or -었드-) to indicate that something happened in the past. Because 갔드랬어요 translates into 갔어요, your example can be translated as "내 마우스에서 나왔죠." (If 마우스 means mouth, "내 입에서 나왔죠.")
South Korea is a small country, where the Internet is available almost everywhere and visiting other regions is generally easy. This makes it natural that people get familiar with various dialects (except for Jeju one). Therefore, it is normal for you to hear dialect words.