Ignore the above Korean comment. His answer is not the correct answer to this question. This phrase is hard to explain the nuance, but I'm sure my comments are the most accurate.

"다며" is just a contraction of "다면서".

If you use "다면서" in a plain form, it means "You said that~",
but if you use it in a questionable form, it means "I heard that~".

So,
"너 잠 잤다면서", "너 잠 잤다며" means "You said you slept".

But,
"너 밥 먹었다면서?", "너 밥 먹었다며?" means "I heard you ate".