According to Mikhail Kizilov in his book "The Karaites of Galicia", there were East European Karaites living in places such as Galicia, but they were not regarded as "Ashkenazim" nor did they speak Yiddish:
"While retaining Hebrew as their leshon ha-qodesh, the Polish-Lithuanian Karaite communities adopted the Turkic Karaimo-Kypchak language in the thirteenth-fourteenth centuries as their Umgangssprache. This feature differentiated the Karaites from their ethnic neighbors - the Yiddish-speaking Ashkenazic Jews, the Slavic Poles and the Ruthenians (Ukrainians), and even from their Tatar-, Greek-, and Arabic-speaking Karaite brethren of the Crimea, the Ottoman Empire, and the Near East." (pp. 10-11)
Paul Wexler similarly notes that the Karaites in Eastern Europe preserved their Turkic language.
However, later on Kizilov writes:
"According to archival data discovered by Dan Shapira, nineteenth century Karaite intellectuals from Volhynia sometimes used Yiddish as a sort of “secret language of savants” which would not be understood by other, less educated, members of the Karaite community. Some Galician Karaites apparently were also able to understand not only Hebrew and Karaim, but also Yiddish, the language of their Rabbanite neighbours. An anonymous traveller (Reuven Fahn?) mentioned that in addition to their excellent command of Hebrew, the Karaites of Halicz could also speak Yiddish. Another report by Fahn also mentioned the fact that most Karaites could speak Yiddish in the 1890s. The Karaites’ ability to understand Yiddish, in addition to their knowledge of Hebrew, Karaim, and Slavic languages, may be explained only by their rapprochement with the Galician Rabbanite Jews. It seems that Yiddish literacy became even more common among the Galician Karaites in the interwar period..." (pg. 167)
Later on in the book (ch. 4), Kizilov lists their customs. The following is a summary of what he wrote:
The architectural designs of the synagogues and tombstones were similar to those of the Galician Rabbanites. The key difference was that their arks and tombstones faced the south, the direction they considered Yerushalayim to be, whilst the Rabbanites' faced the east. (pg. 138)
They did not celebrate Chanukah because it was post-biblical. (pg. 139)
They did not necessitate a minyan for prayer; often there were, indeed, less than ten people in synagogue during prayer times. (pg. 140)
Both men and women wore tzitzit and tallit gadol (unlike in the east, where they wore only tallit gadol). (pp. 140-141)
At least from the 19th century they had mezuzot on the doorposts. (pg. 142)
Circumcision took place on the seventh day, in the synagogue. After the circumcision, the chazzan took a drop of the child's blood and smeared his forehead with it. There was no priah and metzitzah. (pg. 143)
Most matzot were made of flour, water, eggs and milk. Four special matzot were, If I understood correctly, inscribed with the words "לחם עני אמן" and "מצה ומרור אמן". (pg. 146)
Strict Shabbat observance, including not warming food and not keeping light/warming fires in synagogues and homes. (pg. 147)
Engagement was via matchmaking. The process included the giving of a dowry by the bride's family to the groom's family. There was also an engagement event called a "kelesmek". The marital ceremony always took place on Thursday evening. There was a chuppah. The whole ceremony - songs and everything - was in Hebrew. Only one song was traditionally sung in Karaim (the Karaite language): "Bu oł bijenc kinimizni kuvanaik (GVKar. “Let us celebrate this happy day of ours”)". (pp. 152-153)
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