In order to manage Blog Search Form in Magento 2 Blog, please go to the Admin Panel > Stores > Configuration > Magefan Extensions > Blog > Sidebar and find Search Form Widget section.
Search Form Widget
1. Enable or Disable the widget.
2. Set the Sort Order to manage the position of the widget on the Storefront. The higher the number of the position, the lower it will be displayed on the Sidebar.
Once you've finished don't forget to Save Config and Flush Magento Cache.
3. Check the blog Search Form out on the storefront.