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There are no settings that you should need to change. Rather, it seems like you are suffering from another issue that is not directly related to layer height.
It is possible that your hotend's heat sink is not being cooled enough, causing heat to migrate up and soften plastic in the heat sink, ultimately jamming it. Depending on your hotend's make, the heat sink should be cooled by a fan that is always on.
Normally, the plastic being fed into the hotend provides some cooling, but printing at a thinner layer height decreases this effect because less plastic is fed into the hotend per time unit.