To search for older asset versions, you will need to have these settings set to true in your ApplicationSettings.properties file:

can-create-asset-versions=true
allow-search-for-previous-versions=true

and depending on whether you would like to have this functionality available to all users instead of just admins:

allow-search-for-previous-versions-admin-only=false

Non-admin users will only be able to see this checkbox if the version attribute is visible to them!

You can add a checkbox to search previous versions of assets when you are using the homepage search using the settings in Admin -> Attributes -> Display Attributes -> Searching -> Homepage -> Update the search settings.

The available settings let you control if the checkbox will appear and if it should be checked by default.