Can we count non-functional Pokeballs? If so, I'll go with the GS Ball from Pokemon Crystal. Just the fact alone that it's used as the franchise's very first event item gets me giddy every time. For those reading unaware, the GS Ball's use in Crystal was to unlock a sequence of events that would lead you to Ilex Forest's shrine and battle a lvl 30 Celebi.
Unfortunately for international players it was never released and was impossible to obtain anyway, as the Goldenrod Pokecenter (originally doubled as a communications center in JP Crystal which also acted as the franchise's first form on online features) was changed into a regular Pokecenter due to the Mobile GB Adapter needed to collect the item never being sent out. You can glitch the ball into the game but it won't do anything on its own, as you need to trigger a flag from the Nurse Joy in that center who gave you the ball, again impossible now unless you jump through convoluted hoops to glitch that as well.
I've been working a good decade to try and finally play through this event, so you can understand that the GS Ball has been in my mind for some time.