iCloud storage full persistent notification

You either need to delete content to free up space or subscribe for more storage. The nags are no different then when your laptop or desktop nags you when your hard drive is nearly full. When the iCloud storage is full, your iCloud email will stop sending and receiving, your backups will fail or become corrupted, other sync’d data like contacts and notes may become corrupted, you may lose photos or other data important to you.

So you must either delete content to free up space, or subscribe for more storage if you want the nags to cease. There is no alternate methods to make the nags go away. And btw, every other online storage service has the same sorts of nags when your allocated space is nearing full (Google, DropBox, Box, MS OneDrive, etc).