What is the ruling concerning money taken in excess after commissioning someone to bring a paper for a certain amount, and then another person brings it for a lesser amount, while the first person claims to have paid the full agreed-upon amount?

Assigning an employee to bring a document falls under the category of agency (wakalah), and it is not permissible for an agent to take anything from the principal's money except with their permission. Therefore, your friend is only allowed to take what he actually spent to obtain this document. Anything beyond that must be returned, along with repentance. The expenses include what he initially spent to extract the document, as well as the amount he paid you if it was part of the customary cost. As for the reward that was requested afterward, it is forbidden and must be returned.