Hutchins Family 1830-1850s in New York State?

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Hello

I'm looking into my GG Grandfather who was based at a seaport called Lymington in Hampshire, UK and brought up his young family there.  There is a hint on Ancestry (with same parent names) that the family may moved to America in 1830s and that the parents may even have originated in the States - the placename Oneida, New York City is mentioned as a possible residence.
Unfortunately there is no record of the family in the first two UK census of 1841 and 1851 - which might confirm the time spent in America.

So far I have pieced together the Hutchins family as follows (with help from Rootschat):

Richard HUTCHINS
Jane HUTCHINS (nee HOUSE)
married Lymington 1818 - from this I assume both b.<1800

CHILDREN

William  b.~1820
Edwin b.~1823
Mary b.~1825
Herbert b.1829 - my GG Grandfather - he was a mariner in the UK after marriage in 1855
This is stage they may have emmigrated?
Emma b.~1837
Barbara Ann  b.~1842


Any help with tracing the family (and Herbert) in America or their voyages would be greatly appreciated.

Thanks

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There is a town in Oneida County, New York called Paris.  On the 1860 US Census, a single Barbara A. Hutchins (b. 1842 New York) is living there with an Alonzo Penner (b. 1830 New York), his wife Emma (b. 1837 New York), and their son Oscar (b. 1858 New York).  Emma Penner is likely Barbara's sister per the dates you provided, and since their first child was born in 1858 this would likely place the marriage date around that time as well.  Alonzo's relative Jackson Penner and his wife Betsey and their children are living next door.  I didn't have any luck searching for the other Hutchins members.