Cannot sign to Apple ID on Mac OS X 10.9.5

I’m trying to sign in App Store on Mac currently running 10.9.5 so I can upgrade it to the newest version and every time I try to put it my Apple ID I get asked to verify on my iPhone. When I do that and allow I get a verification code which there’s no space to put it in! If I add it after the password or if I put my password I keep getting a message that I forgot my password and that I’ve entered it incorrectly more than once and I need to reset! 

This is driving me crazy! The Apple ID works perfectly on my iPhone 

Ant help is much appreciated