We need to check if the given R group (side chain) corresponds to the named amino acid.
(A) Tyrosine (Tyr, Y): Its side chain is a p-hydroxybenzyl group. The formula is -CH\(_2\)-C\(_6\)H\(_4\)-OH. This match is correct.
(B) Cysteine (Cys, C): Its side chain contains a thiol group. The formula is -CH\(_2\)-SH. This match is correct.
(C) Serine (Ser, S): Its side chain is a hydroxymethyl group. The formula is -CH\(_2\)-OH. The R group given is -CH\(_2\)-CH\(_2\)-S-CH\(_3\). This R group actually belongs to Methionine (Met, M). Therefore, the match with Serine is incorrect.
(D) Asparagine (Asn, N): Its side chain is the amide derivative of aspartic acid. The formula is -CH\(_2\)-C(=O)-NH\(_2\). This match is correct.
The incorrectly matched pair is (C).