Check Statement (I): Metallic radius of Al vs Ga

Normally, on moving down a group, atomic/metallic radius should increase. So one may expect: $r(\mathrm{Ga}) > r(\mathrm{Al})$

However, in group 13, gallium comes after the filling of $3d$ orbitals. The $3d$ electrons shield poorly, causing greater effective nuclear charge on the outer electrons of Ga. This is known as d-block contraction.

As a result, Ga has an unexpectedly small atomic/metallic radius, and in fact: $r(\mathrm{Ga}) < r(\mathrm{Al})$

Therefore, the statement

"The metallic radius of Al is less than that of Ga" is incorrect.

Check Statement (II): Ionic radius of $\mathrm{Al}^{3+}$ vs $\mathrm{Ga}^{3+}$

For the ions $\mathrm{Al}^{3+}$ and $\mathrm{Ga}^{3+}$, gallium again experiences the effect of poor shielding by $d$-electrons before ion formation. Standard ionic radii show: $r(\mathrm{Ga}^{3+}) > r(\mathrm{Al}^{3+})$

Hence, $r(\mathrm{Al}^{3+}) < r(\mathrm{Ga}^{3+})$

So Statement (II) is correct.

Conclusion

• Statement (I): Incorrect
• Statement (II): Correct

Therefore, the correct option is: $\boxed{\text{C}}$