Malta to Rome Italy Flying customs

Malta is in both the Schengen zone so no passport check in Rome, and in the EU so no customs. But reading between the lines about whether you pick up luggage, it sounds like you might be taking a connecting flight there. Is that the case? If so, to where? And is it all on a single ticket?

Sam
Thank you. I am flying on Malta Air Lines to Rome on a separate ticket. Then Delta, Rome back to Atlanta on separate tickets. I did not book complete trip with Delta.

If on separate ticket then very likely you have to get your luggage and check it again unless Delta and Malta airline have some cooperation like Delta has with KLM. You will have to go through passport control in Rome because you are leaving Schengen country.

In which case your luggage will only be labelled as far as Rome.
No Immigration (passport control) or customs when you land in Rome
But you will have to collect your luggage in Rome, find the Delta check-in desk and check in again, handing over your luggage again. And then go through exit passport control as you are leaving the Schengen Area.

Thanks to All for your help
Jim