After my truck has been running I turn the key off and open the door my radio stays on indicating there is still power on in the truck. Does anyone have any idea of the fix for this issue?

 

Welcome to the site..

Does the power cancel exiting/opening the passenger door?

 

Yes it does.

 

Sounds like the door ajar switch attached the door latch.
They collect debris and stick.
You might try using a light lube, lock lube, silicon etc and spray the latch point in the door jamb liberally and open/close the door repeatedly. Sometimes they work loose quickly, sometimes it takes repeated applications and eventually they work loose, or may require the trim panel and latch removed for a replacement switch install. Lubes like WD40 tend to work, but dry back out quickly...