Step 1: Recall what the test detects.
The sodium nitroprusside test on a sodium fusion extract detects sulphur. A red-blood or violet colour appears when sulphide ions are present.
Step 2: Understand the chemistry.
Fusing a sulphur-containing organic compound with sodium gives \(Na_2S\). The sulphide ion then reacts with sodium nitroprusside to form the coloured complex.
Step 3: So we need a sulphur-containing amino acid.
Only amino acids that contain a sulphur atom can give a positive result.
Step 4: Screen serine, threonine and leucine.
Serine \((HOCH_2CH(NH_2)COOH)\) and threonine carry hydroxyl groups but no sulphur, and leucine has only C, H, N and O. None of these can give the test.
Step 5: Check methionine.
Methionine, \(CH_3-S-CH_2-CH_2-CH(NH_2)-COOH\), clearly contains a sulphur atom in its side chain.
Step 6: Conclude.
On fusion methionine yields sulphide ions, which react with sodium nitroprusside to give the red-blood colour.
\[ \boxed{\text{methionine}} \]