I want to remove present Apple ID which exists with America Number which is not working in India

Your cousin will have to remove their Apple ID. This is what your cousin needs to do→What to do before you sell, give away, or trade in your iPhone, iPad, or iPod touch - Apple Support. You cannot do it; only your cousin can do it.

If the phone is SIM locked to AT&T they will also have to ask AT&T to unlock it.

If you mean that the phone is activation locked, only the Apple ID and password used to arm this theft deterrent can be used to remove it. If it is your Apple ID just enter its password. If it is not yours you will have to find the person that enabled it.

If you mean something else please explain.

I’ve posted answers 3 times. From here on you are on your own.