Bektashism and Alevism were originally one denomination, the Alevis are the Levites, the priestly tribe and the Bektashis are the Israelites, the commoners, yet today, many Turkish Alevis are members of members of the Bektashi order so the boundary between Alevism and Bektashism is definitely blurred.  

The Ahi (Hebrew for My Brother) organization is associated with the Bektashi order and organizes male professionals throughout the cities of Anatolia. The women’s branch is known as Bacı (Hebrew: Bati meaning My Daughter). These two ancient organizations formally maintain their Roman/Byzantine names Ahiyan-ı Rum (Hebrew: Acheinu of Rome, Our Brother of the Roman Empire) and Bacıyan-ı Rum (Hebrew: Bateinu of Rome, Our Daughter of the Roman Empire). The Ahi and Bacı organizations are documented since the 13th century CE but are most likely far older than that.

Bektashism is similar yet distinct from Alevism and is organized hierarchically in the manner of Sufi orders. The reason for this is that medieval Sufism emerged from ancient Bektashism which is far older than the Sufi orders which only emerged in the 12th century CE.  Thus was the hierarchical Bektashi order the model for the Sufi orders and certainly not vice versa. There is nothing Muslim about the Sufi hierarchical organization which is about maintaining secret esoteric religious knowledge, a specialty of core Median Judaism. Alevism is also hierarchically organized as led by a hereditary high priest. 

The Khorasani mystic after which Bektashism is named, Haji Bektashi Veli (1209-1271), who by no means founded the ancient Bektashi order is often depicted with the Lion of Judah and the Deer of Naftali as esoterically symbolizing the future reunification of the Southern Jurisdiction of Judah and the Northern Jurisdiction of Israel (i.e. Median Judaism.) Most Bektashis live in Turkey but there is also a vast Bektashi minority in Albania which numbers in the double digits percentage. The world headquarters of the Bektashi order lies in Albania. Bektashism warmly welcomes new converts.