Step 1: Identify the relevant Article.
Article 68 of the Indian Constitution deals with the time for holding elections to fill a vacancy in the office of Vice-President; Article 68(2) covers vacancies arising due to death, resignation, or removal of the VP.
Step 2: State the constitutional provision.
Unlike some constitutional offices with fixed timelines, Article 68(2) uses the open-ended phrase "as soon as possible after the occurrence of the vacancy" - no specific number of months is prescribed for filling a VP vacancy.
Step 3: Eliminate other options.
There is no constitutionally fixed "3 months" or "6 months" deadline for a VP vacancy; "at any time" is too vague and incorrect; the correct constitutional phrase under Article 68(2) is "as soon as possible," making option (3) correct.
\[ \boxed{\text{As soon as possible}} \]