Millie:
yes indeed. A Granddaughter of John Maier said he was 8 years old when they came to America. This would make it around 182 or 1863. However, on census he indicated he came in 1868.
William Frank had 2 known sons, John & George. I would think both were named after family of William.
I have not found them in 1870 but I expect they were also in NY.
By 1880 they are in Franklin Co., AR. GD said they moved from a northern state to Arkansas because land was cheap.

Thanks for the lead. I'll put your notes in the tree or future research.