Does the discrepancy between the actual work schedule and the one recorded in the university's systems affect the permissibility of the salary, and is the salary permissible if the quorum of teaching hours and administrative tasks for faculty members is not met, even though they have not refused any work assigned to them?

There is no sin upon you, and what the official writes will not affect your salary, as long as you do not refuse any assigned work. This is because a special employee (Ajeer Khas) is entitled to full wages by making himself available during the period, whether he works or not; because he has fulfilled his obligation, and his hire is for dedicating himself to the workplace during working hours.

Al-Zayla'i Al-Hanafi said in "Tabyin Al-Haqa'iq": "The special employee is entitled to wages by making himself available during the period, even if he does not work." Al-Marghinani said in "Bidayat Al-Mubtadi": "The special employee is one who is entitled to wages by making himself available during the period, even if he does not work, like someone hired for a month for service or to herd sheep." Al-Nawawi said in "Rawdat Al-Talibin": "If the employee makes himself available and a period for potential work passes, the employer is obligated to pay the wages." Al-Bahuti said in "Kashshaf Al-Qina'": "The special employee is entitled to wages by making himself available, whether he works or not; because he has fulfilled his obligation." It is stated in "Al-Mawsu'ah Al-Fiqhiyyah": "The special employee: is one who works for a specific employer for a temporary task, and his contract is for a period, and he is entitled to wages by making himself available during the period, because his services became due to the one who hired him during the contract period." As for what the official writes, if it is within what the law authorizes him to do, then there is no harm in it. Otherwise, the matter should be rectified according to the labor system and regulations of the university.