The name “Jason” appears in several mythological and fictional contexts, so it’s important to clarify which Jason is being referred to in order to answer this question. In this answer, I will assume that the question refers to Jason of the Greek myth of the Argonauts, who is most famously known for his quest to obtain the Golden Fleece.
In the Greek myth of Jason, he does not possess immortality. However, there is a connection between Jason and immortality through his connection to the goddess Medea.
Medea was a powerful sorceress and the daughter of King Aeetes, the ruler of Colchis. When Jason and his crew of Argonauts arrived in Colchis seeking the Golden Fleece, Medea fell in love with Jason and used her magic to help him complete the tasks that were required to obtain the Fleece. In return, Jason promised to marry her and take her with him when he returned to Greece.
After obtaining the Golden Fleece and escaping from Colchis with Medea’s help, Jason and Medea traveled to Greece and began a life together. However, their relationship was not without its difficulties. In one famous episode, Medea tricked Pelias, the king of Iolcus, into killing his own daughters by convincing him that she could restore his youth and vitality if he boiled his daughters in a cauldron of magic herbs. Medea’s treacherous actions were in part motivated by her desire to protect Jason and their children from Pelias, who had threatened their lives.
Later, Jason and Medea’s relationship deteriorated further, and Medea took revenge on Jason by killing their own children. She then fled to Athens, where she was granted sanctuary by King Aegeus.
Although Jason himself did not possess immortality, the story of Jason and Medea highlights the power of magic and the dangers of making promises that one cannot keep. In the end, Jason’s quest for the Golden Fleece brought him great glory and success, but it also brought him into contact with powerful and dangerous forces that ultimately led to his downfall.