If a person masturbates in Ramadan, what is the ruling on making up prayers and fasting for the subsequent days, especially if he did not know that it necessitates ghusl and does not remember the number of days he spent in this state?

If someone masturbated during the day in Ramadan, unaware of its prohibition, their fast is valid. However, if someone prayed while in a state of major ritual impurity (janabah), unaware of the obligation of ghusl (ritual bath), there is a difference of opinion regarding the validity of their prayer. Ibn Taymiyyah does not consider re-performing the prayer obligatory. Ghusl is not required merely by masturbation unless the emission of semen is confirmed. Doubt concerning the validity of an act of worship after completing it has no effect. Fasting while in a state of janabah and not performing ghusl is valid, as long as nothing that invalidates it is committed. Therefore, it appears that you are not required to make up any prayers or Ramadan days, as the matter is merely a doubt.