Me and my husband lived in a apt for 4 years when the lease was up we turned in the notice on the 3rd of the month the apt took our deposit and charged us back rent and charges I have never heard of can they do that

When did the lease expire (the actual date) and when did you give notice? What state are you in? What did the lease say about notice of termination?

Yes, what does the lease say about notice, iknow where I rent, you have to give a 60 day notice, others require 30 day notice ?
When did you give notice to, if you gave it on the third ? To the 30th of the next month ? Or the end of that month ( less than 30 day)