In Mahabharata Was Arjun killed by his own son?

Yes. Arjun was actually killed by his son, though later revived. Here's the story... of Arjun and Babruvahan. Babruvahan was Arjun and Chitrangada's son. He was adopted by his maternal grandfather and reigned over the kingdom of Manipur. After the great war, when Yudhishthir performed Ashwamedha yagna, Arjun followed the horse let loose to roam over various kingdoms. The horse is stopped by Babruvahan and a battle ensues between father and son in which Babruvahan kills Arjun. Repenting his action, and wanting to kill himself for his heinous action, Babruvahan is stopped by his step mother Ulupi, the naga princess, who gives him a special gem which restores Arjun's life.