You can get the caseSystemId using the caseId. It is not possible to fetch the caseSystemId using the custome fields.
User the below API call to acheive the caseSystemID -
If using postman collection v1.3 - SEQ-3: Get the system ID of a case
if using postman collection v1.5 - SEQ-case-retrieve: Get the system ID of a case
Can you please elaborate a bit more on your concern, so that we may understand what exactly are you trying to acheive?