As a follow up, has eugenics been used in either discourse or practice exclusively by white people for white people (as this question assumes)?

It might help if you explained where you read that Thomas Jefferson supported eugenics, and in particular, what views that source meant to describe by "eugenics."The word "eugenics" itself was coined a century after Jefferson's time so obviously he wasn't saying he supported "eugenics" as an idea.

Are you asking if he theoretically opposed inter-racial reproduction, and yet fathered mixed race children?

Jefferson

Having kids with slaves was common at the time. It was so common that Jefferson's mistress Sally Hemings was his wife's half-sister. Martha Jefferson's father long-term mistress was his slave Betty Hemings, an affair that resulted in multiple children including Sally. Betty herself was the daughter of a slave mother and White father.

It is said that Sally Hemings and Martha Jefferson had a clear family resemblance. They did share a father after all.

White Eugenics

One modern example is the North Carolina Eugenics Board which forcibly sterilized thousands of people in the decades following WWII.

Many of the victims of the NC program were Black, but not all of them. Sterilization was used as birth control and forced on the disabled.

NPR has written some great articles on the NC Eugenics Board including this one and this one on payments for victims.