i cant install any free app since i change the country of my existing apple account to the US store, whenever i want to install a free it asks me for payment verification which prevously befor i changed the country of my account. need help badly

Are you currently in the US ? If not then you cannot use the US store. If you are in the US, then what happens when you put your US payment details on your account - you should be able to remove it after entering it, and the card shouldn't be charged if you are only downloading free items (you may see a temporary store holding charge on the card, which your card issuer should remove within a few days or so).

When you change country (and you have to be in a country to use its store, that is part of the store's terms) you are likely to be asked to enter payment details (which need to have been issued by a bank in that country) : Why can’t I select None when I edit my Apple ID payment information? - Apple Support

When you change the country or region of an existing Apple ID, you must provide a payment method and update your billing options. If you want to remove your payment method after you change the country or region, you can change your payment information to None.