Is it permissible to pray Fajr twenty minutes after hearing the Adhan due to re-praying the Salat on account of white discharge (Qassah Al-Bayda')?

Prayer must be performed before its time expires. For Fajr, this is at sunrise. As for performing it at the beginning of its time, right after the Adhan (definition), this is recommended, not obligatory. It is permissible to perform the prayer at any part of the extended time without sin. Therefore, there is no harm in delaying the performance of the prayer by twenty minutes after its time has begun, as long as it does not result in the prayer's time expiring.