Is there any minhag or halakha to light candles for Mordechai and Esther on Purim?

Some have this custom. The two candles are lit during the Purim seudah.

Sources:

כ״כ הגרח״פ ברוח חיים תרצה, א (קי, ג) ובמועד לכל חי לא, מה (רסב, ב).