iPhone 3 cannot login with existing Apple ID Phone: iPhone 3 or iPhone 3GS
iOS: 6.1.6

I tried to login to App Store , iCloud and iTunes with an existing Apple ID, it shows the below alert:



I’ve done that multi factor login from my MacBook to iPad and vice versa. But on my iPhone it does not work. It doesn’t give me an option to type in the 6 digit verification code. What should I do? I don’t mind resetting it.
You need to enter:

[Your Password][Your Verification Code]


into the password field (without the brackets).

For example, if my password was TerriblePassword and my verification code was 123456, I would enter:

TerriblePassword123456


Source: Apple's Support Page (Thanks @redarm!)