How to improve resolution using 0.3mm nozzle?
knowing that the min layer height can be 1/4 the size of the nozzle?


I'm not sure if that is a limitation of your printer specifically, but going "down" there is really no hard limitation to the layer thickness ratio that I know of or have experienced myself.  At least not on modern printers using standard stepper motors and 1.75mm filament (older 3mm printers were more limited on this).

Going "up" you will hit a hard limit at around 3/4 of your nozzle diameter, as layers will have a hard time bonding to each other past that, and the wall surface will be very corrugated (but I take your question about "best settings" is about making the print better, so with thinner layers...)

If you print at reasonable (as in: not too fast) speed and have calibrated your extrusion properly, you should be able to print at any layer height your printer supports, the limiting factor normally being the mechanical precision of your printer / the gearing of your stepper motor.

In particular, you should try to print at layer heights that are multiple of the distance your printer will travel upwards for each step of your stepper motor. 

Simplifying a bit how stepper motors work: say that your screw raises 8mm for each revolution of the stepper motor, and your stepper does 200 steps per revolution... your printer will raise 8mm/200 = 0.04mm per step.  If you print at 0.05mm, most layers will be 0.04mm, with 1 in 4 being 0.08mm to compensate for the lost 0.01mm at each layer.  This will produce noticeable defects in the print.

The information on how your Z axis is geared is seldom available in the official specification sheet, but usually there is always somebody knowing it on the printer user forums.

As for "best settings", those depends typically from the type and brand of filament being used, as well as from the 3D model geometry.  Printing slowly is always a good idea though, as it limits the "noise" on the print due to vibration.

In your particular example, threads (which are substantially a very long overhang) will actually benefit from a high ratio between nozzle width and layer height (so a larger nozzle or a lower layer height).  This is because, the overhang angle being the same, higher ratios will give more material to extrude onto at each layer.  You can visualise this by thinking to how easier is to offset a stack of books compared to offsetting a stack of dice.