Step 1: Recall the classification rule.
An $\alpha$-amino acid is basic when its side chain carries an extra basic group, so the molecule has more amino than carboxyl groups.
Step 2: Examine alanine.
Alanine's side chain is a plain $\mathrm{-CH_3}$, giving one $\mathrm{-NH_2}$ and one $\mathrm{-COOH}$, so it is neutral.
Step 3: Examine glycine.
Glycine's side chain is just $\mathrm{-H}$, again one amino and one carboxyl group, so it is neutral.
Step 4: Examine asparagine.
Asparagine carries an amide $\mathrm{-CONH_2}$ side chain; an amide nitrogen is essentially non-basic at physiological $\mathrm{pH}$, so it counts as neutral.
Step 5: Examine lysine.
Lysine has a long $\mathrm{-(CH_2)_4NH_2}$ side chain with an extra basic amino group, giving two amino groups against one carboxyl. That makes it basic.
Step 6: Conclude.
The basic $\alpha$-amino acid is lysine, option (B).
\[ \boxed{\text{Lysine}} \]