As far as I know of the Janissaries, they were christian slave boys taken and forcefully converted to Islam and served has elite soldiers for the Sultan. I also know they belonged to the bekhtashi order which was a shia sufi tariqa. My question is why would the Sunni Sultan forcefully convert these kids to Shia Islam? Especially since they were at war with the Shia Safavids for a large chunk of their reign?
The Bektashi order is not Shi'a. They're a bit more syncretic than other Sunni Sufi orders, in that they revere Ali and his family more than is common, but to classify them as Shi'a would be a mistake. See Taşköprüzade's entry on Hajji Veli Bektash in his "Shaqa'iq al-Nu'maniyya". He's very adamant (in the 16th century at least) that the origins of the order have nothing to do with the Shi'ism and innovative beliefs that they're commonly accused of.