What is the period of limitation prescribed for taking cognizance of an offence which is punishable…

Section 468 fixes limitation for taking cognizance only for offences punishable with fine only (six months), with imprisonment up to one year (one year), and with imprisonment above one year up to three years (three years). No period is prescribed for offences punishable with more than three years' imprisonment, so the answer is "No limitation". A special statute may still lay down its own limitation.

Current law: From 1 July 2024 the corresponding provision is BNSS section 514. Section 531 saves specified proceedings pending at commencement under the CrPC.