Start by researching all the Joseph candidates to see which one married Jessie Logan. Further back you have the info from previous posts to the effect that John Hancock and Hannah Addsetts had 3 sons, Thomas who mar Ann Garside 1820, John who mar Millicent Amelia Garside 1812 and William who mar Mary Kelk. Thus two brothers married two sisters. The beginning of the Garside/Hancock - Hancock/Garside problem seems to be when Millicent gave birth to the son she baptised Joseph Garside, she married John Hancock a few months later and presumably Joseph grew up using either or both names, and in no particular order.
So, a Joseph Garside Hancock mar Jessie Logan March qtr 1888 Cambridge. 1901 census Peterborough all Garside Joseph 61 b Worksop, Jessie 41 b Manchester, Amelia b 17 Hull, William 16 b Pontefract, Mary 9 b Northampton, Joseph 7 b Gt Yarmouth, Frank 2 b Gravesend. 1891 census Thrapstone, Northants Joseph 47 b Worksop, Jessie 34 b Leeds, Chas 13 b Hull, Theresa 11 b Hull, Amelia 8 b Hull, Wiliam 6 b Pontefract. This suggests Joseph already had children when he married Jessie. GRO birth reg index Joseph Garside 1893 Yarmouth mother's maiden name Logan, Joseph 1891 Northampton mother's maiden name Logan, Amelia Hancock Garside 1883 Lincoln mother's maiden name Spurr. Joseph Hancock Garside mar Elizabeth Spurr Sept 1881 Lincoln. Either or both marriage certificates will give you the name and occupation of Joseph's father.
Back a generation. 1861 Worksop census all Hancock Joseph 49, Mary Ann 51 b Doncaster, Eliza 18, Millicent 13. 1851 Worksop census all Hancock Joseph 38, Mary Ann 40, Sarah 11, *Eliza 11, *Joseph 8, Melicent 6, **Eliza Lockwood 42 visitor b Doncaster. 1841 Worksop census all Hancock living next door to one another Mary Hancock 45, Henry 20, Ann 20, Sarah Ann 2, Mary 2m. Joseph 25, Mary Ann 30, William 9, Sarah 1. Thomas 20, Alice 20 Edwin 1.
*per GRO index mothers maiden name Davison
https://www.freereg.org.uk/search_records/5818525fe93790eb7f958c70/mary-ann-davison-joseph-hancock-garside-marriage-nottinghamshire-worksop-1831-03-07?locale=en ** Eliza Davison bpt 28/8/1809 Doncaster dau of Geo and Mary C Davison
Have a play, draw up some trees and have a go at eliminating other Josephs. Good luck