I believe I have found where he does belong in the tree. This is his father https://www.wikitree.com/wiki/Arthur-852 per birth and census records.
"New York, New York City Municipal Deaths, 1795-1949," database, FamilySearch(https://familysearch.org/ark:/61903/1:1:2WYL-14S : 10 February 2018), Charles S. Arthur, 03 Jul 1884; citing Death, Manhattan, New York, New York, United States, New York Municipal Archives, New York; FHL microfilm 1,373,949.
"United States Census, 1850," database with images, FamilySearch(https://familysearch.org/ark:/61903/1:1:MZM3-H1Y : 12 April 2016), Charles S Arthur in household of Dorinda Arthur, Ossining, Westchester, New York, United States; citing family 593, NARA microfilm publication M432 (Washington, D.C.: National Archives and Records Administration, n.d.).