If they are not mapped to the schema what's the point of creating custom fields on external objects? I have tested with a checkbox field and verified that my changes are not being preserved, as expected.
Refer Define External Objects documentation, where it specifies the need of creating custom fields.
If the external system allows it, we recommend that you sync the external data source to automatically create related external objects. You can instead choose to manually define external objects to customize the external object names and manually create the custom fields.
Also, think about creation of indirect lookup. Refer: Large Data Volume - Design your data model trailhead.
When you create an indirect lookup relationship field on an external object, you specify the parent object field and the child object field to match against each other, selecting a custom unique external ID field on the parent object to match against the child’s indirect lookup relationship field, whose values are determined by the specified External Column Name.