I think it's a myth, I also have heard it long ago, and up to now, there is no research evidence to support this claim. Also, someone that I know having such a skin problem definitely will be advised by people around to avoid eating milk and fish together or some other restrictions. But, we know that it's truly untruth and have to tell them not to believe in such a thing unless there is a restriction from a doctor or a scientific evidence.
The white patches on skin occur due to a fungal infection or destruction of pigment-forming cells called melanocytes in certain parts of the body, usually face or hands. Both fish and milk together or individually cannot result in any kind of skin disease.
The scientific research study on skin lightening, depigmentation, hydroquinone, retinoid... in review article "Facial hyperpigmentation: causes and treatment".
There is no scientific evidence of that. But there is no logic for that. And in many countries, they are cooked in a same dishes or served together. But skin discoloration in the long term has not been reported yet.