Is it necessary to repeat the ghusl if yellowish-white discharge continues to be emitted after performing ghusl?

A woman's purity is recognized by one of two signs: dryness or the white discharge. If she sees purity by either of these, she must perform ghusl. Any yellowish or brownish discharge she sees after that is not considered menstruation, based on the saying of Umm Atiyyah: "We did not consider yellowish or brownish discharge after purity to be anything." Your fast is valid given the situation you described. There is no specific duration for yellowish or brownish discharge; rather, a woman performs ghusl immediately upon seeing purity and does not pay attention to what she sees after that. However, if blood returns within a fifteen-day period, then it is menstruation.