The Kentucky birth index lists Herbert F. Winkleman, born 16 Oct 1916 in Breathitt Co. (a misindexing of Rowan Co.
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The Kentucky birth index lists Franklin Winkleman, born 15 Oct 1915 in Rowan Co., mother’s maiden name Piety Maze. (It is a delayed certificate, filed in 1944, which is why it is not misindexed as Breathitt Co. like most of the births in 1912-1918 are.
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Judging by his Social Security record, those two records are almost certainly for the same person:
The SSDI lists Franklin Winkleman, born 15 Oct 1916, died 11 Oct 1998, last residence Cincinnati, Hamilton Co., Ohio.
Notice that the birthdate on the Social Security record for Franklin is one day before the recorded birthdate for Herbert F. Winkleman. Apparently the delayed certificate filed in 1944, perhaps in order to get Franklin recorded as his first rather than middle name, gave the wrong birth year. Also, there is no death record for any son of John and Piety dying between 1915 and 1920.
The Ohio death index lists Franklin Winkleman, born 15 Oct 1915 in Kentucky, died 11 Oct 1998 at long-term care facilities in Sharonville, Hamilton Co., Ohio, married, mother’s maiden name Maze, occupation machinist.
The 1916 date is probably the correct one, both because it is the date on the original birth record, and because he was recorded as age 3 in the 1920 census.