The correct order of electron gain enthalpy with negative sign of F, Cl, Br and I, having atomic number 9, 17, 35 and 53 respectively, is

As we go down the group in periodic table, atomic size increases, force of attraction for the added electron decreases. Thus, the added electron becomes loosely bound. Hence, electron gain enthalpy decreases down a group.

$\mathrm{X}\left(\mathrm{g}\right)+{\mathrm{e}}^{-}\stackrel{ }{\to }{\mathrm{X}}^{-}\left(\mathrm{g}\right)$

Actual order is Cl > F > Br > I

The fact that fluorine has a less electron gain enthalpy than chlorine seems to be due to the relatively greater effectiveness of 

2 p-electron in the small F-atom to repel the additional electron entering the atom than 3p-electrons in the larger Cl-atom.