Hello. Thank you for contacting the Toolset support.
As Toolset Blocks view do not support taxonomy views yet, so you need to create both taxonomy archive and another view to display the child categories using the classic views (which it seems you already using it).
So, once you successfully created the taxonomy archive, you need to create another view that query your taxonomy and add the taxonomy parent filter from the Query filter section to "Select taxonomy terms whose parent is the current taxonomy archive"
Taxonomy parent filter
Select taxonomy terms whose parent is the current taxonomy archive.
Then, add the content whatever you want to display to the Loop Editor section and save your view and later add this view to your taxonomy archive page outside the archive loop.
Please let me know if you require further help with this issue.