Dear Sri Brajesh Jha,
I did not notice any reply to your question as to whether
there is any critical edition of the Agni-purana, even though it was posted a while ago. No, there is not a critical edition of the Agni-purana as far as I know. However, purana specialist R. C. Hazra discovered in 1951 the genuine Agni- or Agneya-purana under the name Vahni-purana. He regarded the available Agni-purana as only an upa-purana, not a maha-purana, because of his study of its contents. I attach a scan of my photocopy of his 1956 article, "Discovery of the Genuine Agneya-purana." He also wrote a long article, "Studies in the Genuine Agneya-purana alias Vahni-purana," which was published in two parts in Our Heritage (Calcutta Sanskrit College), vol. 1, 1953, pp. 209-245, and vol. 2, 1954, pp. 77-110. He had begun to prepare a critical edition of this purana. I do not know if he was able to finish it or not; but if so, it was never published. Fortunately, Anusuya Bhowmik took up the task of editing this purana, and it was published in 2012 by the Asiatic Society, Kolkata, in the Bibliotheca Indica Series, no. 336. It is titled: Vahni-puranam also referred to as Agneya-puranam. In this book, the long article by R. C. Hazra, "Studies . . .," is reprinted as the Introduction. This edition is based on four manuscripts, giving variant readings in footnotes. So although it was not called a critical edition on the title page, it can be considered a critical edition.
Best regards,
David Reigle
Colorado, U.S.A.