It sounds as if you are only looking online...? Have you tried to search/get ACTUAL NY death records for Patrick Joseph Connell between 1911-1915?
Here are four possibilities
Surname Given Name Age Death Date Certificate County Soundex
Connell Patrick 49 y Jan 4 1913 373 Kings C540
Connell Patrick 48 y Jun 21 1913 19565 Manhattan C540
Connell Patrick 55 y Jan 4 1915 538 Manhattan C540
Connell Patrick D 58 y Apr 5 1912 10986 Manhattan
Do you know his birth date/year? Have you found him in the 1910 US Census?