In this answer at the end, it says that the Mahdi will kill the Dajjal. I wonder if it is believed that Isa (peace be upon Him) will come back? If so, then what will be his (mission)? Will he kill the Dajjal? If not than will the Mahdi? which one of them will kill the Dajjal?
Dajjal is a controversial topic among Muslim scholars. There are different interprets about it. Some say it is a system and not a person and some say he is a person. But there are some hadith saying there is not only one Dajjal but more than one and there will be many Dajjal starting after prophet. for example this this hadith says some of who saw prophet SAWW can see a Dajjal after death of prophet SAWW:
"I heard the Messenger of Allah(s.a.w): 'There was never a Prophet after Nuh but that he warned his people about the Dajjal, and indeed I shall warn you of him.' Then the Messenger of Allah(s.a.w) described him for us, and he said: "Perhaps some of you who see me, or hear my words shall live to see him." They said: "O Messenger of Allah! How will our hearts be on that day?" He said: "The same
Reference of hadith: Jami` at-Tirmidhi > Chapters On Al-Fitan
Shia scholars believe the Dajjal in this hadith who some of Scholars see him is Muaviyeh or Umayyad Kings. (Ref)
About Jesus a.s. at revolution of Mahdi a.s. it is certain that Jesus a.s. will come and will pray behind Mahdi a.s. and will support and help him and many of Christians will convert to Islam when seeing Jesus a.s. praying behind Mahdi a.s.
- Hudhayfah reported that the Prophet (‘s) said, “Al-Mahdí will turn his face to Jesus when he descends as if water were dropping from his hair, and will say to him, ‘Go ahead and say the prayer.’ Jesus will say, ‘The prayer has been set up only for you.’ So, Jesus will pray behind a man who is among my sons.” (Siràt al-Mustaqím, 2, 257) (ref)
Imam Mahdi a.s. will have an army with 313 top commanders and himself is leader. It is possible that Imam Mahdi a.s. send Jesus a.s. to a mission about fighting Dajjal. In this case it is correct if said any of them fight Dajjal.
Please note there are both authentic and non-authentic hadith about Mahdi a.s. and it is hard to determine details of what will happen.
But assuming it is authentic there is no problem is somewhere is said Dajjal will be killed by Mahdi a.s. and in some other place said will be killed by Jesus a.s. because Mahdi a.s. is leader and Jesus a.s. a supporter or commander of Mahdi a.s.
It is like that when a minister do a mission it can be attributed to president as well.
References and more study:
Jesus through Shiite Narrations (Chapter 11 Second Coming)