How would a hard quota system work? Mirror the US population at large seems the most logical. If so, Asians would see their enrollment at Harvard radically reduced.
As of the 2010 census, Asian Americans make up 5.6% of the US population.
https://en.wikipedia.org/wiki/Demographics_of_Asian_Americans
According to the Harvard 2017-18 Common Data Set, Asians make up 20.7%, 1,388 out of 6,701, of the degree seeking undergraduates at Harvard. Some of them will be from other countries, but most likely, not enough to make a significant difference between 5.6% and 20.7%.
https://oir.harvard.edu/files/huoir/files/harvard_cds_2017-18.pdf