Radheya Karna was a student of Dronacharya and he used to study with Kauravas, Pandavas, Princes of Vrishnis and Andhakas in his Gurukula. He was extremely jealous of Arjuna and did friendship with Duryodhana and used to mock Pandavas. When he saw Arjuna getting appreciation and becoming better than him, he went to Drona to teach him Brahmastra which he taught only to Ashwathama and Arjuna. Seeing his bad intentions for Arjuna he rejected to teach him Brahmastra. Then he left the school of Dronacharya and went to Parshuram where he lied about his identity so whatever he was taught was wasted as Parshuram cursed him for lying and said he would forget his knowledge when he would need it the most.
Karna was indeed trained with Kauravas and Pandavas in Gurukula of Dronacharya. In TV serials, all the mocking and bad behaviour done by Karna in Gurukula towards Arjuna is given to Ashwathama when he never mocked anyone.