My maternal grandfather was this Mailey who lived in Chicago most of his life. He was born in Poland (or Latvia or Russia?)in 1879 but emigrated to the US, perhaps before 1890.
His mother was Melvina.I don't know his biological father's surname, he died when J.J. was young. Melvina married a "Mailey," who became J.J's stepfather. J.J. married Catherine Allen from Cork, Ireland.
They had six children: Eleanor, Dorthy, Fredrick, Catherine, Florance and Ruth (my mother).