On adding \( AgNO_3 \) to KI, \( AgI \) will form, and the solubility of \( AgI \) is very low. As a result, only \( Ag⁺ \) will remain in very small quantities in the solution. The majority of the \( I⁻ \) ions will precipitate out as \( AgI \), leaving very few ions in solution.
Thus, the correct answer is \( Ag⁺ \) ions only.