According to the sources, isoelectronic species are atoms and ions that contain the same number of electrons . To determine if a pair is isoelectronic, we calculate the electron count for each ion based on its atomic number ($Z$) and its charge:

1. $Mn^{2+}$ and $Fe^{3+}$: Manganese ($Z=25$) loses two electrons to have 23, and Iron ($Z=26$) loses three electrons to have 23. They are isoelectronic .
2. $Fe^{2+}$ and $Mn^{2+}$: $Fe^{2+}$ has $26 - 2 = 24$ electrons, while $Mn^{2+}$ has $25 - 2 = 23$ electrons. Because their electron counts differ, they are not isoelectronic .
3. $O^{2–}$ and $F^{–}$: Oxygen ($Z=8$) gains two and Fluorine ($Z=9$) gains one; both result in 10 electrons .
4. $Na^+$ and $Mg^{2+}$: Sodium ($Z=11$) loses one and Magnesium ($Z=12$) loses two; both result in 10 electrons .

Therefore, the pair $Fe^{2+}, Mn^{2+}$ does not constitute an isoelectronic pair.