The Index template is only intended to be used as a fallback. Usually, the “Home” and “Blog” pages will be used instead (depending on wether your homepage is set to “Static Page” or “Recent Posts”).

You can read more details about this issue on this other support thread.

If you are trying to create a custom Page Template to assign to only some of your pages, you can head to Site Editor > Templates > All Templates, as seen below:

Once there, click on Add New > Custom Template:

After creating this new custom template, giving it a name and working on its layout, you will be able to assign it to any page in the editor itself:

Custom page templates can also be added via the “Quick Edit” feature in your page list:

Much obliged for your clear explanation.