He had a son born from a Makara. When Rama and Lakshmana were kidnapped by Airavan and Mairavan, Hanuman reaches to Patala to rescue them. He sees Makaradhwaja. Hanuman introduces himself as Rama's messenger and inquires who he was. To this question, he replies as follows:
When Hanuman burnt Lanka with his tail and extinguished the fire with the help of ocean water, he spat phlegm in his throat caused by the smoke. That was consumed by a Makara present in the ocean. From that, I was born.
Hanumān reaches the demon city under the disguise of a sage and meets
(and fights with) his son - Makaradhvaja. When realization dawns upon
both father and son of each other’s real identity, they call off the
Makaradhvaja recounts his mother's narration of his birth. When
Hanumān burns down Lanka after his tail is set on fire, he reaches
out to the sea to cool it off, in the process he expels few drops of
his sweat into the sea, which are swallowed by Makaradhvaja's to be
mother, and that virile discharge from Hanumān, infallible in nature
owing to his devotion towards the Lord, Śrī Rāma, led to Makaradhvaja's
conception and birth later on.
Yes, Hanuman did have a son called Makardhwaja. The story goes like this, after setting Lanka on fire after meeting Sita, he dipped into a river to cool down. During cleansing, Hanuman's seed fell into the water and was consumed by a reptile named Makardhwaja.
Ahiravana, brother of Ravana and king of the nether world, in search on Hanuman came across this reptile and killed it. During the process, they found a child inside the reptile and called it Makardhwaja as well. On witnessing his strength and skill they appointed him as the guard of the nether world.
Later, when Hanuman was trying to save Rama and Lakshmana from Ahiravana. He faced Makardhwaja in front of the gates of the nether world. In order to save his master, Hanuman defeated his own son in battle.
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