Trouble updating Apple ID settings

I need to update my IOs and the iphone 7 keeps on asking me to type in my Apple ID password, but as soon as I type it in, the field disappears and again, it asks me to type the password in. Sometimes, I can type fast enough to hit continue, but then, again, it disappears and asks me to type. It is a vicious loop that I cannot get out of

I tried to log out of my icloud account as per a previous suggestion, but I cannot type in my Apple ID password for that either.