@Inknut77,
First thing, do not use the secret menu calibration as an "easy out" first step to address your issue. It may TEMPORARILY appear to fix the problem, but the problem will keep coming back.
Your problem is likely just a little oxidation in the pot that is actuated by the J3 stick.
The first level of remedy is simply to vigorously "stir" the stick around to attempt to loosen and remove the oxidation.
The second level is to use some plastic safe contact cleaner, and more stirring, to see if that helps.
The third level of remedy is to actually replace the stick assembly with a new one. Once you do that, it may require use of the "secret menu" FC calibration to get the board calibrated to the new stick.
Unfortunately nearly ALL the You-tube videos that supposedly show how that calibration is done, are WRONG. This link leads to a you tube video that at least will not mess up your controller. The video is for an ST10+. The steps are the same except the ST12 also has a K3 and an S1. Ensure the K3 is centered, similar to the centering of K1 and K2. (You don't really care, for a Q500. It does not use K3 and S1 anyway.)
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There is also a written version of the calibration that covers some potentially useful items that even the video above does not include:
Calibrating ST10 and ST10+ Flight Control Board.