I have an old mechanical watch, from about 1940. If you llok inside, the little wheel that oscillates (the "balance " wheel) has tiny little screws in the periphery. Did a watachmaker actually move these screws in and out to adjust the timing of the watch? That must have been very time consuming-so, was an accurate watch a very expensive item in those days?
If I understand what you are describing on the balance wheel, it consists of a series of little “screws” located around the periphery of the wheel. These are to balance the wheel; please do not move them.
While I don’t know the exact movement that you have, almost all movements have a little lever with a + and - located on a nearby scale. By moving the lever you adjust the watch to run slower or faster.
If you don’t know what you are doing, try a google search on “watch adjustment”