The appearance of white patches on goldfish are an indication of a parasite(s) infecting the fish, most probably protozoan in nature.
Before starting treatment I strongly suggest you have the water tested for levels of ammonia, nitrites and nitrates as water quality issues are the number 1 cause of fish disease.
Test results should indicate ammonia and nitrites=-0- and nitrates 20ppm or lower.
If the results indicate that ammonia and/or nitrites are present in any amount then they would need to be eliminated prior to administering medicine as their presence will negate any positive effect the medicine will have.
Ammonia and nitrites can usually be lowered/eliminated via daily 15%-25% partial
water changes and by cutting down on the amount of feedings. If you don't have a test kit handy you can bring a water sample to your local pet shop and they will usually test for free.
Keep in mind that both ammonia and nitrites are harmful and often lethal to fish. At lower levels they cause the fish to be stressed thus lowering their immune system thereby making them more susceptible to disease and at higher levels will outright kill the fish.
Once the water parameters have been confirmed and rectified if necessary it's time to begin a treatment plan. To start off add 1 tabelspoon of aquarium salt per every 18 litres of water in the tank as parasites do not take kindly to salt.
After adding the aquarium salt remove any carbon media in the filter as the carbon will filter out the medicine I'm going to recommend. Also make sure to remove any live plants in the tank as the medicine will have an adverse effect on them.
Begin to treat the fish/tank with a medicine called Malachite Green, see link below for a view of the product, which is an excellent anti-parasitic medicine. It can be easily found at most pet stores. Treat the fish for two weeks using the directions on the product label as a guide for dosage levels.
If you encounter difficulty in obtaining Malachite Green locally, listed below is a link to an alternative medicine called Waterlife Protozin.
Please keep in mind that the best preventative against fish disease is weekly 25% partial water changes.
Best wishes and please let me know if you have any questions.