The profile of Hanover Clayton was created without any sourcing. The lone source previously cited was an annotation "Ancestry Family Trees Publication" without link or reference number. This profile was linked as a child of Prudence (Lanckford) Clayton, wife of William Clayton. Both William and Prudence have been exhaustively studied and there are no records whatsoever for a child with the name of Hanover. The Claytons did have a daughter Hannah and it is possible that "Hanover" was a typo or a conflation.
A search of Ancestry.com and FamilySearch.org reveals MANY unsourced family trees showing Hanover as the child of William and Prudence. On Family Search, there are 22 records for Hanover as the child of William and Prudence and each one is cited as an unsourced "Pedigree Resource File" (a link to a member-generated family tree) or a link to an unsourced Ancestry.com tree.
There are NO SOURCE RECORDS WHATSOEVER for any person named Hanover Clayton, born anywhere, in the mid-17th century. It appears that this record was created once, likely by accident, and has been re-copied and repeated again and again. Records exist for the other children of William and Prudence and it is probably impossible that the creator of the original unsourced tree had access to birth records that are not included in the database that contains the remaining (actual) members of the family.
Additionally, some of the trees show that "Hanover" migrated to the new world and died in Nothingham, Chester, Pennsylvania in 1737. The Clayton family was prominent in Chester, William was even on the Pennsylvania Provincial Council and was a judge in Philadelphia. It would be nearly impossible for a member of the Clayton family to migrate to Pennsylvania and die some three decades later and escape being recorded on a single Quaker Monthly Meeting record.