What is the ruling on joining a master's program through "intercession" in admission, knowing that admission was based on fulfilling the preliminary conditions and passing the written exams, and that the field of specialization relies heavily on favoritism and nepotism?

There is no blame on the questioner for the intercession he sought from his professor, as he fulfills the conditions for admission to the master's program and has not infringed upon anyone's right. Furthermore, the potential intercession in the oral exam is not forbidden due to the prevalence of favoritism and واسطة (connections/mediation) in this field. The questioner is advised to disregard these whisperings and strive diligently in his studies.