How to override admin
To override file of admin theme, You can create your own admin theme by making parent theme as a magento default admin theme (Magento/backend).
Follow below tutorial for create your own admin theme.
As you have created Magento Backend Theme.
Copy the below File from Magento Vendor Directory:
Create equivalent directory structure in your custom backend theme and paste the footer template file:
Yes as mentioned you need to make a child theme of your current theme. Basically it uses all the files of your current admin theme (extends) until you add in an override file into your child theme (footer.phtml).
If you search around there are some zip files containing a full child theme ready for you to customize.
See the following answers: