What special reward is there for a first wife who is patient when her husband marries another woman, and is it greater than jihad, with evidence for this?

There is no authentic evidence that proves a special reward for a woman whose husband marries another, and the narration that mentions she receives "a reward like that of a martyr" is weak.

However, a woman's patience in obeying her husband in general is a reason for entering Paradise. And her patience with her husband marrying another has special rewards:

1. The reward of patience in the face of tribulation: Her husband marrying another is considered a tribulation, and her patience with it expiates sins and elevates ranks. 2. The reward of ihsan (doing good): If she responds to that with ihsan towards her husband and his other wife, she will receive the reward of those who do good. 3. The reward of suppressing anger: If she feels anger but suppresses it and refrains from speaking ill, she will attain the reward of those who suppress anger and forgive people.

A wise woman should be content with what Allah has decreed and know that polygyny is permissible. It is wrong for her to object to what is permissible more than she objects to what is forbidden. She should emulate the wives of the Prophet and the female Companions in patience and seeking reward from Allah. This life is a test, and happiness is for those who are patient in obeying Allah to attain everlasting bliss.