Hello, I am looking for a book about Persian during Parthian and Sasanian rule. Unfortunately book list doesn't have such books.
Daniel Potts' 1999 book The Archaeology of Elam contains chapters on Parthian and Sassanian sovereignty in ancient Iran. Potts is an incredible scholar who knows his material well, so the writing is a bit dense. The focus is also on archaeological material, but Potts is able to intersperse historical information seamlessly into his narrative. A full bibliography (upto the book's publication) can give you places to read further.
That's an area of scholarship that in general remains a desideratum(part of the problem is that the source material on Sasanian Persia is scattered across at least five languages plus much very understudied archaeological material. as well as the common perception that it was a period when nothing very interesting happened). Potts is a very good book in general; you could also look at Parvaneh Pourshariati's The Decline and Fall of The Sasanian Empire although you would be well advised to read that book carefully and judiciously. You may also want to read the chapters of Richard Hovannisian's The Armenian People from Ancient To Modern Times, vol. 1 dealing with the Parthian and Sasanian periods because the Armenian sources are among our more important sources on the Sasanian Empire. Last, I would suggest having a poke around the website Sasanika.org; it has several decent bibliographies, primary sources, and a number of fine short articles, translations of selected primary sources, and lectures.