Is it permissible to refuse financial compensation for overtime hours in exchange for occasionally leaving before official work hours, with or without the knowledge of the supervisor, in a government institution?

What you have agreed upon with your supervisor regarding leaving work is permissible if your supervisor is authorized to do so by his workplace. As for your leaving without the supervisor's knowledge, it depends on the agreement made between you. If the agreement allows you to leave once the additional work is completed, then there is no blame upon you. Otherwise, you must seek permission and inform the supervisor.