Apex Legends FPS Drop On PC when trying to use Controller to MKB Mapping

I was having a similar issue as you. I'm using a PS navigation controller with a mouse and Xpadder. Every time I would ADS with the controller a stutter was introduced while I was aiming. What fixed it for me was removing the "xbox 360 controller" from my devices and printers menu. Give that a try and see if it helps.