The amino acid that gives a red-blood colour on treating its sodium...

Methionine is the only amino acid among the given options that contains sulphur.

During sodium fusion, an organic compound containing both nitrogen and sulphur forms sodium thiocyanate ($NaSCN$).

This extract gives a blood-red colour when treated with $Fe^{3+}$ ions due to the formation of ferric thiocyanate, $[Fe(SCN)]^{2+}$.

Although the question mentions sodium nitroprusside (which typically yields a violet colour with sulphide ions), the blood-red colour specifically confirms the presence of both nitrogen and sulphur. Therefore, methionine is the correct choice.

Answer: methionine