Was Josias called Joseph in America. If so, you probably have this for him:
Joseph Redman and Elizabeth Davis, married 18 Feb 1830, Posey Co, IN
also indexed as Joel Redman. no image available at ancestry.com
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1830 Census, Black Township, Posey County, IN
Joes Redman household
1 white male 20 to 30
1 white female 20 to 30
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an Edward Readman, age 75, died 25 Jan 1913, Mt Vernon, Posey County, son of Joseph Readman, unknown birth place, and unknown mother, born Posey County IN
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are you sure Edward Redman, born 1763, husband of Hannah Brockhurst and Jane Greenfield, lived until 1831? This looks like his son Edward with Jane in the household. On the same page of the 1830 census as above
Edward Redman
free, white males:
1 under 5, 1 5 to 9, 1 20 to 29,
free white female:
1 under 5, 1 15 to 19, 1 40 to 49
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This might be Mary Redman, b 24 Oct 1808:
Mary Redman, married Zimri Mills, 30 April 1826, Posey County, IN
A tree for Mary (Redman) Mills and children. The tree says she died in 1837. no source given.
https://www.familysearch.org/tree/person/details/MFG3-S3Ya tree at ancestry says Mary Ann Redman, b 24 Oct 1808, Billinghurst, Sussex, died 17 July 1838, in Posey County. no spouse known, no source given. The same tree said that Edward and Jane had a daughter Anna, born 1804. Is that correct?
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Last thought - if you haven't already done so, you should try looking through the 1830 census of Black Township, Posey County, In. You can probably browse it at familysearch, I'll see if I can find the starting page in a minute.
You might find Elisha or Jessie as heads of a household, but indexed so poorly that they doesn't show up in a search.