Thanks for using Apple Support Communities. I can see from your that you have two-factor authentication enabled for your account. It sounds like you want to remove this because you receive frequent request from a device that you already have signed into with your Apple ID. As it turns out, if your account was created in iOS 10.3 or macOS Sierra 10.12.4 and later, you can't turn off two-factor authentication.
However, you can learn about ways to manage your trusted devices so that you have a more seamless experience. Check out the link below.
Two-factor authentication for Apple ID
Regards.View and manage your trusted devices
You can view and manage a list of your trusted devices in the Devices section of your Apple ID account page.
- Go to your Apple ID account page.
- Sign in with your Apple ID.
- Go to the Devices section.
The device list shows the devices that you're currently signed in to with your Apple ID. Select a device to view the model, serial number, and other useful information, including whether or not the device is trusted and can be used to receive Apple ID verification codes.
You can also remove a trusted device. Removing a trusted device will ensure that it can no longer display verification codes and that access to iCloud, and other Apple services on the device, is blocked until you sign in again with two-factor authentication. If you need to find or erase your device before you remove it from your trusted device list, you can use Find My iPhone.