It may be from the overflow passage. This opening in the sink
leads down to the drain (stopper). The passage often fills up with
mucky soap scum which is a breeding ground for mold.
There's no good way to clean it out, but you might try a
turkey baster filled with bleach solution to force it in
the passage and kill the mold for a while.
It's also possible that mold is growing in the scum present in the
drain just below the stopper and before the trap. I've seen some
cases which resisted attempts to kill the mold until the drain
was actually taken apart and swabbed clear of the scum.
You don't say where you live. If the sewer roof vent gets plugged it can
force sewer gases back through the drains. This can happen for a variety of
reasons, but if you are in a cold area it is especially likely during
freezing weather with lots of precip.
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