Is a partner entitled to claim 50% ownership of an electronic application because he paid 50% of its programming cost, despite a prior agreement on a lower percentage of profits due to his non-participation in the work? And what is the ruling on dissolving the partnership with him by returning the paid money and his share of the profits, especially if he refuses except for an exorbitant مقابل [counter-payment/compensation] or with the intent of revenge?

If it is agreed that your friend will pay 50% of the application's price, then he is a 50% co-owner of it, and the profit will be according to the agreement. A partnership is a permissible contract, and either partner may dissolve it. In that case, the application is valued at its market price, sold, and its price is divided according to the ownership percentage, in addition to each partner's share of the profit. If both partners want to buy the application, the way to decide is by drawing lots.