There is an 8 yr old female M C in the workhouse.
http://www.census.nationalarchives.ie/pages/1911/Galway/Ballinasloe_Urban/Society_Street/448481/
Birthplace was "Born in House".
The only Connor baby registered with a forename beginning with M who was born in Ballinasloe Workhouse in 1902 or 1903 was Mary 31st October 1902 as previously noted. (I tried Mary, Margaret and Martha. Any more names beginning with M?.) No female Connor babies registered without a first name. No Josephine.
Ballinasloe R.C. baptisms after 1900 not online. Ballinasloe, Diocese of Clonfert, County Galway and Roscommon.
https://registers.nli.ie/parishes/0324 Click on "Irish Ancestors" for full list of years.
