Can a man who has one testicle and is unable to marry due to a health problem resort to masturbation as an alternative, and what is the legitimate solution for such a case that leads to frustration and abandoning work?

The accuracy of the doctor's prognosis is unknown. Masturbation is not a solution as it is forbidden. We advise relying on Allah and getting married. If marriage is not possible, then follow the guidance of the Prophet, peace be upon him. Be patient with Allah's decree, for every decree for a believer is good for him, and "No disaster strikes except by permission of Allah. And whoever believes in Allah - He will guide his heart. And Allah is Knowing of all things." Have a good opinion of Allah and seek treatment, for He is capable of healing you. Face your life with optimism and strive in your work; perhaps Allah will remove this affliction from you and grant you marriage and offspring.