What's this cognitive bias that relates to misremembering exact stimuli? Say a participant is shown a reference stimulus of white colour. Afterwards, they are shown a number of test stimuli that range from yellow to blue like this (yellow -> less_yellow -> whitish -> white -> less_whitish -> blueish -> blue) and they are asked to note which one is identical to the reference stimulus

In my experience, the participant is likely to underestimate, and pick the stimulus before the actual "white", but rather somewhere in the area of "whitish". This may be because they're shown stimuli that progressively go towards the target they are looking for, and they are worried they might miss it, and every new stimulus looks more and more like the reference stimulus.

Anyone knows of a psychological bias that relates to this?

Edit: After going through some lists of cognitive biases, contrast effect is similar to what I am referring to, but it does not relate to other facts such as fear of passing the threshold.

Edit2: Less-is-better effect seems to be related to this too.
As opposed to the contrast effect which relates to stimuli that are presented simultaneously or in immediate succession, the similar distinction bias constitutes a possible/partial explanation for the phenomenon that you conjecture: stimuli are experienced as more distinct when presented simultaneously than when they are presented separately.

Another bias that may play a role here is anchoring, which describes the tendency to take that piece of information which is presented first in some context as a reference.

Note that this applies to (perceptual) judgement, not so much to memory/misremembering (but I think that this is what your question is actually about).

I am sceptical regarding the observation of underestimation being more likely. It is possible that some worry to miss leads to a hasty decision, but isn't it equally possible that a more optimistic participant has an opposite tendency, missing the correct stimulus? This will depend on the design, too – it should make a difference whether the displayed series just starts with the yellow sample, shows the blue sample before starting with the yellow, shows the whole continuum before starting at either end, etc.

In general, the accuracy of perceptual judgement is the subject of signal detection theory which considers tendencies to falsely miss a present target stimulus, or to falsely rate an absent target stimulus as present. Signal detection theory explicitly includes response bias and reasons why responses may be either liberally or conservatively biased.