I have a 15 speed that make a clicking noise once every tire revolution and only when the chain is on the 4th sprocket (2nd smallest).
It does not matter what front sprockets is used.
It does not matter if I slightly change the rear derailer as I ride.
But, it does need some pressure, like going up an incline.
If I put the bike on a repair rack to test it, the noise is not there.
All this happened after I cleaned and greased the rear bearings and replaced the chain and Freewheel.
BTW:This bike is in very good shape, not a junker.