Statement-1: Electron affinity values of the 3rd period elements on extreme right of the periodic table except noble gases are generally more than the 2nd period element of the same group.

Statement-2: Due to smaller atomic size of the 2nd period element, its electron density increases which eases the addition of electron.

This is energetically unfavorable due to electron-electron repulsion, which increases the electron affinity. Contrary to what the trend would have you believe, the Period 3 elements actually have the highest electron affinities.
When an electron is added to an atom of oxygen or a molecule of fluorine, the additional electron moves to the lower n = 2 energy level and is strongly attracted to the other electrons in this level. Because the electron in S or Cl moves up to the higher n=3 energy level and fills up more space as a result, there is significantly less electron-electron repulsion.