white patch on the fish & fish became hyperactive

Not sure if that's ich, as usually it presents as little white dots all over. That looks more like some other kind of fungus or possibly an ulcer type thing to me, although only one of your pics worked so it's hard to tell. Let us know the following so that the folks here can better help you treat your fish illness!

Housing
What size is your tank?
What temperature is your tank?
Does your tank have a filter?
Does your tank have an air stone or other type of aeration?
Is your tank heated?
What tank mates does your betta fish live with?

Food
What type of food do you feed your betta fish?
How often do you feed your betta fish?

Maintenance
How often do you perform a water change?
What percentage of the water do you change when you perform a water change?
What type of additives do you add to the water when you perform a water change?

Water Parameters:
Have you tested your water? If so, what are the following parameters?

Ammonia:
Nitrite:
Nitrate:
pH:
Hardness:
Alkalinity:

Symptoms and Treatment
How has your betta fish's appearance changed?
How has your betta fish's behavior changed?
When did you start noticing the symptoms?
Have you started treating your fish? If so, how?
Does your fish have any history of being ill?
How old is your fish (approximately)?