The janissary (jeni cseri = new army) is a response to the halt in turkish conquest. Their cavalry armies were not suited for siege warfare in the Balkans: forts were much more common then in their native lands and they needed infantry for the fights.
Their first try was a semipro/semi regular infantry, the jaja/pijade troops, but in field battles they proved to be a liability because of their lack of discipline. The result was the establishment of the janisseries (new army) which slowly took the place of the jaja (the janissery officers kept their old name "jajabasi"). The very first janisseries were most likely an order of dervishes, which later gained numbers with the "devshirme" a tax of young boys, which had to be "payed" by christian populace of the balkan provinces from about the 1380's.
The janissary corps was founded around 1360 (but with low numbers, about 1000 men), and they remained at the back seat - the jaja remained main infantry - until about the end of the 14th century. We know that the jaja were main infantry at Nicopolis,1396), but Mehmed I (1402-) used mostly janissaries, not jaja. (maybe the jaja rebelled against Mehmed during the interregnum?)
That means that in the game the ottomans shouldn't be able to recruit janissary troops at all if is earlier then 1360ish, then they should be available in very low numbers. The increase in number should happen around 1380, and it should only happen if the turks have Balkan provinces which are orthodox (devshirme was a tax for christians)
It would be interesting for a muslim nation to have a unit which requires 51% orthodox faith

(but it will be out of scope of 3.0 anyway)