A form data provider may be enhanced by the customer with additional fields. However, it depends on the individual form data provider whether an enhancement is possible, as SAP has to enable the enhancement option.

Enhance a form data provider as follows:
In the SAP Fiori Custom Fields and Logic app, open the Custom Fields tab and choose New.
In the Business Context field, select the appropriate business context.
Enter the field's properties.
Choose Create and Edit to add the new field.
Enable the field for selected forms.
Typically, the field must also be enabled for selected UIs so that data can be entered.
Otherwise, no data would be displayed in the extended form.
Sometimes there are Business Add Ins (BAdIs) for key-user extensibility that could fill these added fields programmatically.

The publishing step may take some time, as several elements are generated then, such as the actual database field, the respective fields in the concerned CDS views of the business context, and so on.

Now you can work with the additional field in a form in SAP S/4HANA, as follows:
Go to the SAP Fiori Maintain Form Templates app.
Download the form.
When the form template is downloaded, you receive an .xsd file with the interface (data connection/data view) and an .xdp file with the form template layout.
- You can find the additional field in the .xsd file.

Upon editing the form template with Adobe LiveCycle Designer, you can find the additional field in the Data View. You can then add it to the layout. At runtime, it will be provided with data. The data has either been entered previously by a user via a UI, or it has been generated programmatically. For example, by a BAdI implementation.