How should I treat my cat’s skin disease?

Hello, from the photo you uploaded, the cat’s symptoms don’t look like ringworm, because the spot is bleeding and shows no dandruff. To check for ringworm, you can use a Wood’s lamp; if there’s no green fluorescence, it’s probably not ringworm, and the damage is likely from scratching. In this case, clean the wound with saline and disinfect with iodine, then see whether it heals normally. If the symptoms don’t ease, take the cat to a vet promptly.