@JOLSKY.... I think your old employer is trying to bully you. Please go to the Ministry of Labour in Isa Town and lodge a complaint against your old company. This will ensure that your rights are protected at all times.
Simultaneously, please have your new employer apply for your mobility and transfer your visa to their company. The question of blacklisting an employee, especially after the employee has left their employment is ridiculous. They are merely trying to bully you. So what if they are working with the Prime Minister's office? Do you honestly believe His Excellency's office has time to get involved in a case of 'employment'?
Take all documents with you, including your resignation letter & acceptance of your resignation by the company and your passport when you visit the Ministry of Labour.
Be brave and dont let them bully you
Best wishes