Apple ID needed for updates

Hello I used to have this old Apple ID I would share with my cousin but I made another Apple ID for him. So then when I go to the App Store there are some apps I downloaded with the old Apple ID i made so I put the password to update them then nothing happens? The update button just comes back... And there is no box saying my password is incorrect and also I logged in my Apple ID on this website so I know the password isn't wrong. What do I do? I don't wanna delete those apps and have to download them with my other Apple ID cause then I will lose all my stuff in those games.