Is it permissible to take the surplus amount from the monthly salary to compensate for a previous period of unpaid work, or what should I do with the surplus amount that is difficult to return to the state?

If the questioner has a right with the entity they worked for, and this entity fulfilled the work according to the stipulated conditions and contract terms, then the right must be claimed openly and through lawful means. If the entity that sent him to study is the same one that denied him his right, then there is no objection to taking the amount of his right from the salary, provided that no employee is harmed. However, if the entity he is affiliated with is not the same one that denied him his right, then he is not permitted to take the money, and he must return it to the concerned entity. If returning it is not possible, then it should be spent on general Muslim welfare and charitable causes.