Is it permissible for me to manage a project that involves applying a fine to those who are late in paying their bills, or is it permissible for me to supervise its completion without direct management?

A fine for late payment of debts is usury (riba), which is forbidden in Islamic law. It is not permissible to assist in it in any way, whether by managing its project or being responsible for its execution, due to the Almighty's saying: "And do not cooperate in sin and aggression." However, there is no objection to working for the company in a position that has no relation to this fine.