Is my breaking of the fast on the third day of menstruation considered valid, based on the appearance of a yellowish discharge on the fourth day, with doubt regarding the source of this yellowish discharge?

You made a mistake by breaking your fast while being pure and having seen the sign of purity (tahara). It is obligatory for a woman, when she sees the sign of purity, either by dryness or the white discharge (al-qassah al-bayda'), to perform ghusl (definition), fast, and pray, based on the saying of Ibn Abbas: "It is not permissible for her, if she sees the sign of purity even for an hour, except to perform ghusl." As for the yellowish discharge on the fourth day, if you are certain of its exit, then its ruling is that of yellowish and brownish discharges (al-sufra wal-kudra), which are considered menstruation during the period of habit, but not otherwise. If you are uncertain about its exit, then the default is that your purity remains, and certainty is not removed by doubt, especially if you are afflicted with obsessive thoughts (waswasah), in which case you must disregard them.