Does anyone know where I might find lists of orphans in this Asylum between the years of 1850 - 1880?

I am searching for my g-grandmother Elizabeth Wogan and any family that she may have had. I have her parents in the 1850 census with no children (Eliza and Michael Wogan). I have her baptism from Tree Talks as being May 13, 1860 at the Church of the Assumption, Syracuse. NY. and a birth date of March 4, 1856 in Syracuse.

Oral history - she was raised as an orphan

Census History as Elizabeth (Lizzie) Martin she is as any orphan unsure of her parentage.

Onondaga Poor House - I find a Michael Wogan (father's name) in and out for intemperance.

Any help/direction most welcome!

Sharon - Western Canada