I think the family came from this Neukirchen:
(maybe there are helpful members in the links)
http://neukirchen.kreis-regenwalde.de/
https://www.genealoger.com/german/pommern/kreis/regenwalde.htm
https://pommerscher-greif.de/kirchenbuch-online/articles/landkreis-regenwalde.html
On the passenger list 1869 of the Ship Gutenberg :
--------------------------------------------------
is a family Schmidt from Neukirchen in Pommern
Dep. Hamburg 1869
Father Friedrich Schmidt . 44 Jahr (* about 1825)
(Fridr. maybe wrong)
Mother Auguste Schmidt - 39 Jahr (maiden name ?) (* about 1830)
Son Wilhelm Schmidt - 15 Jahr (* about 1854)
Son August Schmidt - 11 Jahr (* about 1858)
Daughter Bertha Schmidt - 6 Jahr (*about 1863)
On the same passenger list is a family REDIESkE
from Muhlendorf in Pommern.
Friedr. Redieske - Father
Louise Redieske - Mother
with 3 children.
This couple Redieske is also mentioned in the churchbook
of Neukirchen/Pommern - so I am sure, that
the family Schmidt came from the above mentioned Neukirchen/Pommern)
(churchbook entry
oo 1856, April 1, Muhlendorf.
Friedrich August Redieske and
Jungfrau Anna Maria Luise Rossow)
In the passenger list the father
Schmidt is called Friedr. ? and
his Wife Augustine. -
maybe Friedrich is wrong ?
please see the following :
oo
Neukirchen 1853, June 3rd
the farm servant
Gottlieb Ludwig Ferdinand Schmidt and
Jungfrau Justine Wilhelmine Henriette Dübke.
their children
1854 Neukirchen
* Februar 21st
~ March 5th
Wilhelm Friedrich Ferdinand
Father Tagelöhner Ludwig Schmidt,
Mother Justine Döbke
* 1858 Jan. 15, Neukirchen
Friedrich August Ludwig Schmidt.
~ Jan. 31, 1858.
Father Taglöhner (daylaborer) Ludwig Schmidt
Mother Augustine Dübke,
Do not hesitate about "Justine" -
August = "french" "Ojüst"
Augustine = "Ojüstin"
Best regads