Andrew Reome, b. USA, 51, day laborer
Hattie, dau, b. USA, 18
Antwine, son, b. USA, 16, day laborer
William, b. USA, 13
Hellen, granddau, b. USA, 10/12ths
In the 1910 Ogdensburg Census Andrew (father), Hattie (dau), Antonie, Wilburn and Helen but no Edgar.
If Helen and Edgar were removed from hattie's care, was that Hattie Andrew's (father) daughter or his wife that hadn't lived with the family since 1905?
I don't think Edgar was adopted in 1918 because he's not on the 1920 Census with Andrew (son) and his wife Josephine. Helen/Helene is living with them and their children.
Andrew Rehoeme, NY, abt. 1880
Josephine, b. NY, 49
Orville, b. NY, 29
Edward, b. NY, 28
Clarence, b. NY, 26
George, b. NY, 23
Laura, b. NY, 17
Edgar, adopted son, b. NY, 20
Patricia Roth, neice, b. NY, 5
I don't think you will find Edgar's adoption information because those records in New York are confidential and under court seal. An adoptee who was born or adopted in New York, the birth parents or biological sibling can register with the Adoption Information Registry to obtain certain kinds of information per New York State Dept. health, https://www.health.ny.gov/vital_records/adoption.htm
I didn't find Helen after the 1920 Census probably because the indexers mangled the spelling of her surname. Since she was 15 then, I don't think she was adopted but probably married young.
All Vital Records after 1880 were originated and filed at the Town Clerk's office with a copy sent to New York Deptt. Health, Vital Records Section. Birth records are restricted for 75 years, marriage and death records 50 years. Successful Searching!