Death Records Now

If he died in 1906, have you gotten his death certificate, or checked to see if there was one? That is the most logical way. Depending on the ages of his children in 1906, if they were minors, they may have a guardian apptd. If it shows to be a brother of his, then you could also try to find a death record for that person (to connect from the side).
It also is possible that the only record you will find with the father, could be the census.
References :

I did a search on http://www.familysearch.org and it came up with a marriage for Johan Osmon to Mary Ann Bretz in 1845 in PA.
I also found this on the site named above.
Isaac Edward Osman
Male
Birth: 21 MAY 1848 Harrisburg, Dauphin, Pennsylvania
Christening:
Death: 16 DEC 1880
Burial:

Parents:
Father: Johan Osman
Mother: Mary Ann Bretz Osman
Children
1. John Bretz Osman
Male
Birth: 01 MAY 1844 Harrisburg, Dauphin, Pennsylvania
Christening:
Death: 06 APR 1863
Burial:

2. Isaac Edward Osman
Male
Birth: 21 MAY 1848 Harrisburg, Dauphin, Pennsylvania
Christening:
Death: 16 DEC 1880
Burial:
References :
http://www.familysearch.org/

Hi Adam, I found your message on the boards at GenForum, and your public family tree on Ancestry! :o)

Have been searching and didn’t get any further than you have – – all the census records I’ve looked at for Osman in PA show PA or NY as birthplaces, even for those born in the early 1800’s. It could be that the Turkey "rumor" is really for an ancestor further back in your family tree:
OSMAN Name Meaning and History
1. Turkish: from the Turkish personal name Osman, Turkish form of Arabic ?Uthman. This was the name of the third of the ‘rightly guided’ khalifs (ruled 644–656), one of the ten Companions of the Prophet Muhammad, to whom he gave the good news of entering into paradise.
2. English: variant of Osmond.
3. Dutch: from a Germanic personal name composed of the elements ans ‘god’ + man ‘man’.
4. Dutch: occupational name for an ox driver, from os ‘ox’, ‘bullock’ + man ‘man’.
5. German (Osmann): variant of Ossmann (see Ossman).
6. Jewish (eastern Ashkenazic): of uncertain origin; perhaps a variant of Oshman or Hausman.

Best of luck, I tried!
References :

http://www.familysearch.org–1880 census
Isaac OSMAN
Other Information:
Birth Year <1847>
Birthplace PA
Age 33
Occupation Farmer
Marital Status–Married
Race White
Head of Household Isaac OSMAN
Relation Self
Father’s Birthplace PA
Mother’s Birthplace PA
Census Place– Shamokin, Northumberland, Pennsylvania

Harriet S. OSMAN
Birth Year <1855>
Birthplace PA
Age 25
Occupation Keeping House
Children: ( Name-relation-marital status-sex-race-age-where born-parents born)
Emma M. OSMAN Dau S Female W 8 PA PA PA
Minnie N. OSMAN Dau S Female W 4 PA PA PA
William F. OSMAN Son S Male W 3 PA PA PA
Alice L. OSMAN Dau S Female W 10M PA

http://www.ancestry.com–1900 census
Name: Isaac Osman,age 53
Spouse: Harriet ,age 47
Birth: abt 1847 – Pennsylvania
Residence: 1900 – Portage, Cambria, Pennsylvania
Others in household:
Name: Treon Charles Osman –Boarder, age 27
William Osman–Son, age 23
Cora Osman–Granddaughter, age 3
Charles Osman–Son, age 14
Elmer Osman–Son, age 17

Frank E. OsmUn–Harriet’s other husband; notice difference in last name spelling.
Birth: 3 Mar 1861 ,Northumberland Co., Pa.
Death: 11 Dec 1914 ,Pennsylvania

Treon Osman
Parents: Isaac Osman & Harriet S. Bordner
Birth: Dec. 1873
(wonder why 1900 census lists him as a "Boarder" if he were their son??)

John Osman (shown as a son here)
Parents: Isaac Osman & Harriet S. Bordner
Death: Shamokin

I don’t know if this is from your submission to ancestry.com, but I found it in their One World Tree pages about Harriet:
Frank E. OSMAN
Sex: M
Birth: 3 MAR 1861 in Northumberland Co., PA
Death: 11 DEC 1914 in PA

Marriage 1 Harriet S. BORDNER b: ABT. 1853 in Shamokin, PA
Married: WFT Est. **1873-1903 (**going just by this year in the estimate, Frank would have only been 12 years old, and Harriet,20–a bit of robbing the cradle, so to speak)

http://www.familysearch.org–1880 census
Frank OSMAN
Birth Year 1862
Birthplace PA
Age 18
Occupation– Coal Miner
Marital Status– Single
Race –White
Head of Household –Charles MARTZ
**Relation Stepson
Father’s Birthplace– PA
Mother’s Birthplace– PA (her name–Matilda)
Census Place– 4th Ward, Shamokin, Northumberland, PA

Alternate spelling of Frank’s last name–OSMUN–shows Jacob OSMUN as his father and mother as Matilda OSMUN. Frank’s occupation, with this last name spelling, is "At Home" , but as OSMAN, he’s a "Coal Miner" at the same age.
References :

A Historical Society in that area is your best bet to get solid answers.
References :

Try http://www.rootsweb.com. You can type in his name in the search area and then go to the WorldConnect result, if you get one, there are lists of family trees that other people did that you might find his name in.

I have family that is from the Enola area and found a lot of good information about my great-great-great- grandparents through the World Connect link.

Also if you go the the Pennsylvania’s Department of Health site they have a whole page with information on how to obtain birth/death/marriage records…I found it very useful.

Good Luck
References :