In 1830 the Karaite ḥakham Simḥah Babovich hired him as a tutor for his children and as his secretary to accompany him in his pilgrimage to the Land of Israel. During their visit to Jerusalem, Hebron, and Cairo Firkovich bought and copied many ancient books. In 1831–32 he moved to Istanbul, where he served as ḥazzan, shoḥet, and melammed. Following a conflict with the community there he returned to Evpatoria (Gozlow), where he organized a society for the publication of Karaite books. In 1834 he was appointed head of the Karaite publishing house there and published his biting anti-rabbinic book Ḥotam Tokhnit, accusing Rabbanites of crucifying Jesus and killing Anan ben David .
In 1839 M. Vorontsov, the governor general of the Novorossya region and the Crimea, addressed a series of six questions to Babovich, who had become head of the Karaite Spiritual Council. These dealt with the origins of the Karaites and the time of their settlement in the Crimea, their character traits, occupations, important personalities, historical sources about their origins, time of their separation from the Rabbanites, and the differences between them. Babovich then recommended Firkovich investigate these questions and the latter initiated his archaeological and other expeditions in the Crimea and the Caucasus, uncovering ancient tombstones and manuscripts in order to produce an account of Karaite history. His main work, Avnei Zikkaron (1872) describes his travels and contains a collection of tombstone inscriptions with several pictures of these tombstones appended. In the course of his work Firkovich created a new concept of the origins of the Crimean Karaites, according to which they settled in the Crimea in 6 B.C.E.; therefore they could not share the responsibility for the crucifixion of Jesus. Firkovich wished to convince the authorities that the Karaites were a separate nation which differed historically, culturally, and anthropologically from the Rabbanites. He was the first Karaite author to apply a "scientific" research methodology to ameliorate the legal status of his congregation. To substantiate his claims Firkovich fabricated colophons and falsified some of the tombstone inscriptions. He changed the real dates on the tombs to earlier ones. He also "invented" some great figures of Karaite history, suchas Isaac Sangari (identified in a late medieval source as the sage ("ḥaver") who in Judah Halevi 's account in the Kuzari converted the king of the Khazars to Judaism). In Firkovich's version, Sangari converted the Khazars to the Karaite version of Judaism and died in Chufut-Qaleh.
Yet within a year of Firkovich's death, a controversy raged over the authenticity of the Firkovich material. Such prominent scholars as A. Harkavy, H. Strack, P.F. Frankl, and A. Kunik claimed that Firkovich's collections abounded in forgeries and fabrications. Even D. Chwolson, his most sympathetic critic, had to admit the general unreliability of Firkovich's manuscripts. Nevertheless, the manuscripts that he amassed were used or published by several well-known scholars in their studies about the Karaites. (S. Pinsker's Likkutei Kadmoniyot (1860) was based on Firkovich's materials; Fuerst and Graetz also unhesitatingly used this material.) Discussions of the authenticity of his materials stimulated the development of Jewish studies in Russia and Western Europe.
His manuscript collection is considered to be one of the most valuable collections of Hebrew manuscripts worldwide. Firkovich sold his first collection containing over a thousand Rabbanite, Karaite, and Samaritan manuscripts and Torah scrolls from the Crimea, Caucasus, and Middle East to the Imperial Library in St. Petersburg in 1862 and in 1870. His second collection, containing over 15,000 items, was sold after his death (1876). Most items originated in the Genizah of the Karaite synagogue in Cairo, which Firkovich visited in 1864. It is the largest collection of its kind in the world. These collections and his private archive, which are housed in the Russian National Library in St. Petersburg, were opened to researchers only after the breakup of the Soviet Union. Most of the material is available in microfilm at the Jewish National and University Library in Jerusalem.
בראשי העמודים: מסה מריבה.
השער בעברית וברוסית. הנוסח הרוסי של השער משולב בנוסח העברי, פסקה אחר פסקה.
בראש הספר מכתב בלשון טאטארית-קראית מאת שמחה בבוויץ, ראש העדה הקראית, גוזלווא, ד אב תקצ"ו.
דף ו: שיר ידידות מאת יעקב וויינבנש, קאמינץ, תקפ"ח.
 דף: תיקוני טעויות ושיר לכבוד הספר מאת יהודה בן משה מאגס, חכם קראי מלוצקא (לוצק). פותח: שישי אש דת שישי וגילי בת מלך.
תוכן הספר: דברי פולמוס ולעג חריפים נגד ההלכה והמסורת הרבנית וכן נגד הדת הנוצרית, בחרוזים.
המחבר ריכך אחר כך כמה ביטויים חריפים, בעיקר נגד הנצרות, ולשם כך הדפיס מחדש כמה דפים. הוחלפו 5 דפים: לב, לד, לז, עה, קג. אך בטפסים שונים שרד לעיתים דף זה או אחר מן ההדפסה הראשונה עם הנוסח המקורי של דברי המחבר.
הדפים המוחלפים נדפסו על נייר גס, שונה בטיבו ובצבעו מן הנייר של הספר כולו.
עיין: י' יודלוב, גנזי ישראל, ירושלים תשמ"ה, מס' 1836; ש' פרנקל, ספר מסה ומריבה לאברהם פירקוביץ צנזורה עצמית או זיוף, בתוך: דברי הקונגרס העולמי הי"א למדעי היהדות, תשנ"ג, חטיבה ג כרך א, ירושלים תשנ"ד, עמ' 242-236 (לדבריה יש גם נוסח
שלישי של דברי המחבר. כנראה אין זה אלא שיפור-הנוסח שנעשה במהלך ההדפסה).