What should a female student do who has entered a university specialization through واسطة (mediation/favoritism), knowing that her total grades qualify her for admission to the specialization, but there were no vacant seats, and her father intervened with the university dean to admit her, and she now feels remorse and fears that she may have taken the place of someone more deserving than her?

There is no blame upon you for entering the mentioned specialization, as long as your grades qualify you for it, and it has not become clear to you that you have taken someone else's right. It is not necessary to know that there is no one more deserving than you, as that is difficult to ascertain. And the fact that your father has no acquaintance with the dean removes the suspicion of forbidden favoritism. And your salary is lawful, Allah willing, as long as you perform your work as it should be.