Filtering tickets using custome fields

I would like to raise a query regarding the filtering of tickets based on custom fields. I have observed that when attempting to filter tickets based on custom fields without options, such as 'cf_external_id,' I receive an empty response. Unlike custom fields with predefined options, filtering based on custom fields without options does not yield the expected results for a custom field with predefined options, the response is successful but empty unlike a custom field with predefined options . Could you please assist me in resolving this issue?