Why does milk turn yellow in a silver glass?
tl;dr It looks like your milk has curdled. It is unlikely to be related to the silver cup.

Milk is composed of casein, albumin proteins, sugar, some amount of fat, and vitamins including riboflavin. The solution of protein and fats is opaque white. When milk is curdled- usually by exposure to acid and/or heat, the casein proteins denature and tangle up much of the fat. They separate into curds and settle out of the solution. The remaining sugar and albumin is transparent in solution. The riboflavin has a yellowish-green tint.

Whey looks exactly like the yellowish liquid in your photo.

In your photo you can just see the wispy white of the casein proteins that have come out of solution.

Silver on its own won't curdle milk. Silver nitrate will if your cup was previously used to hold nitric acid but I sincerely hope that isn't the case.
It's more likely that your milk spoiled enough to curdle or was exposed to some other acid unrelated to the silver cup. It is possible, if you haven't used this cup before, that the seller used an acidic cleaner to remove tarnish before selling it.