We check each proposed test of $\mathrm{K}_4[\mathrm{Fe}(\mathrm{CN})_6]$ (potassium ferrocyanide) with the given cations.

Statement (A): $\mathrm{CuSO_4} + \mathrm{K}_4[\mathrm{Fe}(\mathrm{CN})_6] \rightarrow \mathrm{Cu_2[Fe(CN)_6]}\downarrow$ Copper(II) gives a chocolate brown precipitate with ferrocyanide in acetic acid medium.

So, (A) is correct.

Statement (B): $4\mathrm{Fe}^{3+} + 3[\mathrm{Fe}(\mathrm{CN})_6]^{4-} \rightarrow \mathrm{Fe}_4[\mathrm{Fe}(\mathrm{CN})_6]_3\downarrow$ Ferric ion with ferrocyanide gives Prussian blue precipitate.

So, (B) is correct.

Statement (C): Zinc salt with potassium ferrocyanide gives a white to bluish white precipitate of zinc ferrocyanide, especially on neutralisation with $\mathrm{NH_4OH}$.

Therefore, (C) is correct.

Statement (D): Magnesium does not give a blue precipitate with potassium ferrocyanide. This observation is not a standard confirmatory test for $\mathrm{Mg^{2+}}$.

So, (D) is incorrect.

Statement (E): Barium with potassium ferrocyanide followed by neutralisation with $\mathrm{NaOH}$ is not the standard test giving the stated white precipitate in this context.

So, (E) is incorrect.

Hence the correct set is: $A,\ B,\ C \text{ only}$

This corresponds to Option B.