My great grandfather William Clarke married firstly ? and had two children , Ernest born in 1889 and John W born 1894. By 1900 he had re-married, Kate Hulse my gt grandma and the couple had moved to Altrincham where my nan was born. William died when my nan was a baby and Kate moved to Northwich in Cheshire, where she originated from.
What happened to the two boys from Williams previous marriage?. I only found out about them on the 1901 census, had no idea nan had two half brothers, I know she never knew about them. Her mother went on to marry a widower in Northwich and had more children with him.

I'm also a clarke from sheffield it can be very tough to find,there's just so many of us and we all had a great grand dad called William,well best of luck in your quest

Spelt Clarke without the e on 1891 census
Name: William Clark
Age: 27
Estimated Birth Year: abt 1864
Relation: Head
Spouse's Name: Agnes Clark
Gender: Male
Where born: Southport, Lancashire, England

Civil parish: Ecclesall Bierlow
Ecclesiastical parish: Golcar
County/Island: Yorkshire
Country: England
Registration district: Ecclesall Bierlow
Sub-registration district: Ecclesall Bierlow
ED, institution, or vessel: 10
Neighbors: View others on page
Piece: 3803
Folio: 33
Page Number: 19
Household Members:
Name Age
William Clark 27
Agnes Clark 26
Ernest Clark 3

What you need to do now is try and trace the boys marriages. The first place I'd try is Cheshire where they grew up. Free BMD is a good site for that.:)