Apple Account login fails with "Failed to verify your identity. Try Again"

It has been almost 2 weeks since I am facing this login issue. I have 2 internet service providers(let's say A & B) and I logged in my apple account when I was connected to A and it went through 2FA and I logged in successfully. Then, whenever I was connected to service provider B and tried logging in, it failed with this error(Failed to verify your identity. Try Again) and it never asks for 2FA or any other option to login except reset password. So, to overcome this nonsense, I used to connect with service provider A before login and it always succeeded. Now, from yesterday, my internet provider A is out of service due to a thunderstorm and I have no option to login. I was already worried what will happen if I go outside of the city but I am in similar situation even at home now.