The "strongest conjugate acid" corresponds to the weakest base among the anilines (a weak base's conjugate acid is strong; a strong base's conjugate acid is weak).

Electron-donating groups (OCH${}_3$, CH${}_3$) increase the basicity of the amine, making its conjugate acid weaker. Electron-withdrawing groups (NO${}_2$) decrease the basicity, giving the strongest conjugate acid.

Basicity order: 4-OCH${}_3$ $>$ 4-CH${}_3$ $>$ aniline $>$ 4-NO${}_2$.

Conjugate-acid strength is the reverse: 4-NO${}_2$-aniline gives the strongest conjugate acid.

$\therefore$ Option (3) — 4-nitroaniline.