Miami University lists the Prodesse Scholarship among the awards open to international applicants. It pays $1,000 to $2,000 a year and renews for up to four years, so the ceiling across a degree is about $8,000.
It goes to selected top students admitted to Miami's Honors College beyond the fifteen named Presidential Fellows each year, which makes it the second tier of the same selection. The Honors College admission decision and the scholarship decision happen together, so the work is in the application itself.
There is nothing extra to file. Submit the Common App by 11.59 p.m. on 1 December and tick your interest in the Honors College. Miami decides all of these scholarships at the point of admission, and how high the academic bar sits depends on who else applies that year.
Keeping it means staying enrolled full-time on the Oxford campus with a cumulative 3.0 GPA. The sum is modest next to Miami's published costs, so treat it as a top-up to a larger merit award rather than the thing that funds the degree.