Story of Hanuman and Aksha, son of Ravana, can be found in the Sundhara Kanda of Ramayana. The story happens after the meeting of Hanuman and Mata Sita.
Hanuman destroys the entire Ashokavana and announces his arrival in Lanka. A story army of 80,000 Rakshasas sent by Ravana is completely overrun by Hanuman.
Then an army led by Prahastha, one of the ministers of Ravana, confronts Hanuman. They too meet the same fate. The young rakshasa prince is killed and the army is destroyed.
Then Ravana summons his son, Aksha. The young warrior wearing an armor of gold ascended the chariot on the command from his father. He went to the place where Hanuman was waiting.
A terrible encounter happened between Aksha and Hanuman. Hanuman was full off praise for the young warrior but he was not ready to ignore Aksha as Hanuman thought that it was unwise to ignore a raging fire.
Hanuman killed the horses of the chariot of Aksha and broke the chariot.
Aksha then rose to the sky and started fighting with Hanuman. Hanuman easily caught hold of him and dashed him to the ground.
Aksha fell down dead.