There are actually a few such programs going on in America. I’m aware of strains where the bees bite off the limbs of mites, and some that are more aggressive towards them.
There is at least want breeder that has managed to get queens that seem to result in mite free hives
(Edit to clarify: resistance to mites isn’t really the problem - the problem is that the mites are very effective at spread more or less all viruses that harm bees, and the feed on the larvae just for good measure. Basically you want bees that actively fight infestation so that they don’t have to become resistant to every single disease)
There is at least want breeder that has managed to get queens that seem to result in mite free hives
(Edit to clarify: resistance to mites isn’t really the problem - the problem is that the mites are very effective at spread more or less all viruses that harm bees, and the feed on the larvae just for good measure. Basically you want bees that actively fight infestation so that they don’t have to become resistant to every single disease)