Must the prayers of the past three days be repeated due to doubt about the nature of a small spot that disappeared from the nail after prayer, and do such cases necessitate repetition?

If you are certain or highly assume that the spot was present before ablution (wudu'), then it is obligatory to remove it or to exert every effort to do so, because one of the conditions for the validity of ablution is that water reaches the skin. The prayers you performed with an invalid ablution must be repeated. This applies to someone who prayed while having thick spots on their nails that prevent water from reaching [the skin]; they must repeat both the ablution and the prayer, as mentioned in the prophetic tradition. We advise paying attention to purity and being cautious of obsessive thoughts (waswas).