Historically, the Seljuk Turks invaded Anatolia also had skilled horse archers, while the Ottomans centuries later utilized gunpowder hence Janissaries, and they also inherited horse archery from their Seljuk ancestors.
The Seljuk period covers Castle Age, while Ottoman covers imperial age.
The main UU should have been a cavalry archer unit, called the Sipahi. It could the extra HP that the existing UT has. The theoretical Castle Age UT (named Akinci) could have another bonus that can benefit cavalry units.
The current UU Janissary could well be better as a secondary Imperial Age unit when Imperial Age is reached and replaces Hand Cannoneer in the Archery Range, while the Sipahi will serve as the main Unique Unit available in the Castle at all times.