I know of using と for noun & noun phrases, て-form to connect sentences Perhaps when speaking English you might suddenly remember something and go 'Oh! And (whatever you remembered).
Another example may be, say, listing, but with something in brackets/aside from the normal list. 'Mum, Dad, Brother (And a cat!)
Maybe you're leaving home for school and your mom may call 'And don't forget to eat your fruit!', or something similar.
Is there a word or particle you would use independently in these circumstances? I have seen this, but none of these words seem to quite fit the nuance I'm trying to forget. I hope this makes sense.