Because I am a stickler for accuracy in language: If they’re a mix, then they aren’t purebred. The word “purebred” means an animal bred from parents of the same breed or variety. Because you have two different breeds involved, they are a mix.
That said…do they go outside? Have you taken a fecal sample to the vet annually? I give heartworm preventative 4x a year – my old man cat doesn’t go outside, and I get annual fecal and blood testing done for him. Get fecals and blood panels done, at the very least, to make sure everything’s good. Without a full picture of your cats’ health, you cannot make an educated decision on how to handle medications and the like.
What do you feed? If there’s any grain or chicken in the food, try something else. You want grain free and something with a novel protein. I would also wash his feet every time he comes back inside and if this persists I would head to a veterinary dermatologist.