1850 Census for Ashland Co, OH has Jacob BARLET 28 b PA; wife "S" 28 b OH; 2 ch b OH 1860 Census for Ashland Co, OH has Jacob BARLET 41 b PA; wife Sarah 40 b PA; 5 ch b OH 1870 Census for Ashland Co, OH has Jacob BARTLETT 51 b OH; Sarah 53 b OH; 2 ch b OH; plus 3 YOUNG ch b OH
Next door in 1860 is Catherine BARLET 64 b PA, etc. Next door in 1850 is P (m) BARLET 60 b PA; C (f) 59 b PA; 2 ch b OH
It's hard to say if this is a BARTLETT or a BARLET family; but I would say they are clearly from PA.It appears they were in OH before 1833 at least.
There is a chance that Jacob's wife Sarah b c1822 OH/PA died and he married a second Sarah who was a widow of YOUNG and she brought 3 children with her.Another theory is that the 3 YOUNG children may have been children of his or her sibling who died or could not raise them.Did you find them in 1880 to see where their parents were born?