Is it obligatory to complete the fast and perform ghusl again upon seeing a bloodless discharge after having performed ghusl from menstruation and intending to fast?

If the questioner ascertains purity by one of its two signs (dryness or the white discharge), then her fasting is valid and obligatory upon her. What she observed of the sign of purity during the day confirms her purity, and she must continue fasting. She is not required to repeat ghusl (ritual bath) for seeing the sign of purity again.