Someone is trying to login into my Apple ID from various cities in various countries

When you press allow a verification code will appear on the screen. The person trying to login won’t have access to that code and won’t be able to finish logging in.

However, you do need to carefully follow Apple’s recommended steps at If you think your Apple ID has been compromised - Apple Support

AkashRohmetra wrote:

I have been getting this constant notifications to allow someone to login into my Apple ID in various cities in various countries and then my ID be a chance when I am using my phone by mistake, I give them the permission , because it suddenly pops up while you are using the phone and my phone and my Apple ID is at risk. Then after I don’t allow consciously, then there is another notification that change your Apple ID password. I am scared if my kids are holding the phone and they allow someone to login into my Apple ID. What would I do?

Hello, AkashRohmetra

This Apple support article will further assist you in Rejecting unknown sign-in attempts – Apple Support. I would also recommend changing your password, and take further steps to Keep your Apple ID secure.

Otherwise, Apple Support would be able to provide you with more guidance for this situation.

Take care