Is there a listing of all of the babies who were born on ellis island back in the late 1800s?

My maternal grandmother was born on Ellis Island in December 1896. She told my mother that, but there's never been any "proof" of it. My mother never knew her grandmother, nor her name or what ship she entered this country on. It wasn't something she questioned her mother on when she was younger and my grandmother died fairly young. My mother is now 82 years old and I would like to trace this part of the family for her as she would like to verify her mother's birth on Ellis Island and find her grandmother's grave. Even if I could find the name of immigrant ships that came to Ellis Island November and December 1896 that would be helpful. Thank you for any information.
Asked Aug 13, 2014

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