unable to log in on old iphone 4, no apple id is log in cause of icloud two factor authentication

To log into your Apple ID with an iOS device running iOS 8.x or earlier, you will need to enter your ID's password, followed immediately by the 2FA verification code that you receive on one of your "trusted" devices. That "trusted" device does not necessarily have to be another iOS device ... and that would have been established by providing a "trusted" phone number when you first enabled 2FA.

Looks like Elitegate provided you an excellent response before I could get back to you. Thanks @Elitegate!

The key is to enter your Apple ID password, immediately followed by the verification code that you would receive on another device. Again, that other device does not need to be an iOS device. It could be an Android or a land-line that you provided the "trusted" phone number for when you enabled 2FA.

He literally gave you the solution. You can use your existing / current Apple ID on your iPhone 4 that is running 7.1.2 or below that. You have the 2FA enabled and entering your Apple ID and password on the iPhone 4 you will recieve that 2FA code on your other iOS device that runs a more modern version of iOS, right? But on your iPhone 4 there is no such prompt to enter the 2FA. I had this problem myself on an iPod touch (4th gen) with iOS 6.1.6.

For a solution you need to login on the iPhone 4 with your

Apple ID (E-Mail)

Password which is then followed by the 2FA

So let's say your Password is ABCDEFGHI and the 2FA is 123456. Instead of just typing the password like you normally would you wanna type in ABCDEFGHI123456.