How do you get the purple Yoshi in Yoshi story n64

There is no purple Yoshi in "Yoshi's Story." There are only green, blue, dark blue, red, yellow and pink. If you are good at the game, you should be able to find the black and white Yoshi's who are also playable.
For proof that there is no purple Yoshi, check the end scene when you finish the game. You see all of the Yoshi's that you have jumping around the tree with two spaces. Black and White fill that space.