With Azure Boards (cloud service), you can choose to copy child work items when copying a work item. For more information, see Copy or clone work items.
This feature isn't supported at this time for Azure DevOps 2019 and earlier versions. Copying a work item doesn't copy any parent-child linked work items. However, is available for Azure DevOps Server 2020.1 update and Azure Boards (cloud service).
The easiest way to accomplish the task of copying many work items with child items is to create parent-child links to new work items using Excel. To learn how, see Bulk add or modify work items with Excel, Add a hierarchy of linked work items.
Other solutions include employing one of the following Marketplace extensions:
Work item form one-click actions
1-Click Child-Links
1-Click Tasks