Since the discovery of antimatter decades ago, particle physicists have wondered if these particles were repulsed by gravity. Einstein predicted that despite having opposite charges to its regular matter counterparts, antimatter should still behave like matter does concerning gravity. This has been tricky to confirm experimentally since it’s hard to make enough antimatter to observe its behavior. Particle physicists have finally pulled it off, using the ALPHA-g experiment at CERN, generating antihydrogen atoms and then dropping them in a 3-meter tall vertical shaft.
[description taken from Fraser Cain’s mastodon post ]
There are no known particles. However, you can get a great foray into negative inertial mass from a PBS Spacetime that was done on the subject.
The answer is, we don’t know, but it seems unlikely as negative inertial mass breaks a lot of well established things. But you never know, could be something we’re missing that “fixes” all the breakage negative inertial mass causes.