Answer
The order in increasing size is $$Co^{3+}\lt Fe^{3+}\lt Fe^{2+}$$
Work Step by Step
$$Co^{3+}, Fe^{2+}, Fe^{3+}$$
Both $Fe^{2+}$ and $Fe^{3+}$ have the same nuclear charge. However, $Fe^{2+}$ has 1 more electron than $Fe^{3+}$, so it has more electron-electron repulsions to screen the nucleus attraction. Therefore, the size of $Fe^{2+}$ is larger than that of $Fe^{3+}$. $Fe^{2+}\gt Fe^{3+}$
$Co^{3+}$ is in the same row with $Fe^{3+}$. Though it has more electrons than $Fe^{3+}$, the higher nuclear charge of $Co^{3+}$ attracts electrons more to the nucleus, making the size of $Co^{3+}$ smaller than $Fe^{3+}$.
Overall, the order in increasing size is $$Co^{3+}\lt Fe^{3+}\lt Fe^{2+}$$
