الجواب حامدا و مصلیا
If the organizers of the Madrasa are approved by the students to be their advocate in receiving Zakat (which is usually done through fulfilling the admission form) or after possessing money given in Zakat through whichever means, uses this money to provide food for the students of the madrasa, then (in this case) the questioner can eat in the kitchen of the Madrasa, even though his father also gives Zakat to the Madrasa.
And Allah knows best.
