Is there any mistake in saying: "O Lord, bestow Your prayers upon our Master Muhammad, prayers by which Yusuf will be cured and safeguarded from all harm and evil," with the intention of healing my sick son?

Praying for the Prophet (peace be upon him) is among the greatest acts of nearness to Allah and the best acts of obedience. It is a cause for the relief of distress and the expiation of sins. Therefore, if you increase in it, using it as a means to seek healing for your child and the removal of your worries, it is good. The mentioned formula has no objection. And seeking intercession through good deeds has an effect on the answering of prayers. It is also recommended to recite ruqyah for the child with the established adhkar and supplications, and the Quran, especially Surah Al-Fatihah, and to continue medical treatment without despairing of Allah's mercy.