The system by which residents of indian villages remained legally free and entitled to wages, but were still required to perform a fixed amount of labor each year was called

Repartimiento system, is the right answer.

Explanation:

A system of forced labor imposed on the natives of Spanish America and the Philippines is known as the Repartimiento system.

In some form, it was just similar to the tribute-labor system of the Inca Empire or the  Ancien Régime France.

It was a system in which the local population was required to give their labor for the colonial leaders in mines, workshops or farms without pay for some days in a year.