How do I display taxonomy child terms?
I used View tree Module to achieve this same kind of functionality but i used it for Node Reference. As per their module page, this module is also compatible for taxonomy.

Here are the steps to set Views Tree to display hierarchical taxonomy.

Create a new term view using the fields row style


add relationship for taxonomy term: parent term
add field term id (do not use relationship) and exclude it from display
add field term id with relationship, exclude from display
add any fields you want to display, like term name, term description, etc...
Change style plugin to Tree (Adjacency model)
Set Main field to Term ID
Set Parent field to Term ID with parent relationship