Ninja Gaiden Sigma
Bringing the classic to the PlayStation 3, Ninja Gaiden Sigma is a more complete version of the Xbox Team Ninja title, with new moves, actions, and weapons for Hayabusa. Also added is a new playable character -- Racheal, one of the series' heroines, will be playable, and when using her, you'll get to experience the storyline from her perspective (with new cutscenes, attack moves and more.)
I recently ordered this and it sent me Ninja Gaiden 2.
no, there are a lot of games that are re-released on PS4 with enhancements, but there is zero backwards compatibility, nothing other than ps4 games can be played on a ps4