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.