I was recently talking with a Muslim acquaintance about similarities and differences between kashrut and halal, and she mentioned something I had never heard before: in her family dairy and fish are separated, exactly as followers of Judaism separate dairy and meat, including not only not eating them in the same meal but even keeping separate dishes. I was fascinated to learn about this. She didn't know whether it was a commandment or custom or where it was sourced from, however, and a very cursory internet search does not turn up any more information. So, first, is this a part of the halal system? And if so, where is its source?
From the point of view of Islamic law, dairy and fish may be consumed together as there is no proven prohibition regarding it.
However it has been said in various books of scholars that it is against the Sunnah, for example Ibn Qayyim's book on Prophetic Medicine (Paraphrased translation):
ومن تدبر أغذيته صلى الله عليه وسلم، وما كان يأكله، وجده لم يجمع قط بين لبن وسمك ... ولا بين لحم ولبن
The Prophet Muhammad ﷺ, in his food, never joined together milk and fish ... nor meat and milk