Your ancestor's surname is Smith, a common name, so he is more difficult to research than someone with a less common surname. If the information on his profile is accurate, he died only one year after the most helpful US censuses began to be taken -- the first being in 1850. It looks like he died in 1851 in Maine, and his son, Henry M. Smith, was born in Edmonds, (apparently Washington County), Maine, USA.
With that said, I am going to paste a link to some FamilySearch results. You can use it to see what I used as search parameters. You may be able to make the search more accurate if you know more than I do about family members. If you DO have more recent ancestors that you have better information for, it is important to fill in the details and sources for the more recent generations (at least through the 1800s.) Is Henry M. Smith your ancestor also? Knowing the provable facts about more recent generations make it more likely that you'll be able to distinguish between other William H. Smiths and your ancestor.
Here is the FamilySearch link (that shows results of my search parameters): https://www.familysearch.org/search/record/results?count=20&query=%2Bgivenname%3A%22William%20H.%22~%20%2Bsurname%3ASmith~%20%2Bbirth_place%3AEngland~%20%2Bbirth_year%3A1783-1785~%20%2Bresidence_place%3A%22Washington%2C%20Maine%2C%20United%20States%22~%20%2Bresidence_year%3A1820-1855~%20%2Bspouse_givenname%3ADeborah~
Here is one result that is likely to be the right Smith, since Henry M. Smith has been linked to the Wikitree profile as a son, and the birth date matches the information provided on the profile.
Name: Henry M. Smith; Gender: Male; Birth Date: 05 Jan 1826; Birthplace: Edmund, Washington, Maine; Father's Name: William H. Smith; Mother's Name: Deborah. (Citation: "Maine Births and Christenings, 1739-1900," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:F4SH-4D7
: 10 February 2018), William H. Smith in entry for Henry M. Smith, 05 Jan 1826; citing Edmund, Washington, Maine; FHL microfilm 10,400.)
I will add the above birth record to William's son Henry's profile as an example to look at, especially since it doesn't have any sources other than a Gedcom import.
Notice that there are birth records for many children of William and Deborah Smith in the results of this search. I didn't look at them individually to make sure that the locations and dates match the profile, but the odds are good that at least some of these are your William's children.