What is the fate of a person who believes that his good deeds and supplications are of no benefit to him in this world, and fears that his fate in the Afterlife will be the same, which has caused him to lose the motivation to continue with acts of worship?

The problem is a demonic whisper, measuring the reward of the afterlife against the reward of this world, and this is one of the most corrupt analogies. This is because the world is a realm of trial and test, and its blessings are not an indication of the servant's honor. The believer worships Allah to attain His pleasure and the reward of the hereafter. The prophets, who are the elite of creation, were subjected to trials. The answer to supplication may not be by fulfilling exactly what was asked for, but rather by expediting it, or storing it for the hereafter, or averting a similar evil. The servant must worship his Lord with fear and hope, for Allah possesses the power to withhold and bestow with His wisdom. Delaying the answer might be for a greater good, or due to a flaw in the servant. You must strive in worship with fear and hope, and be certain that Allah does not waste the reward of those who do good deeds.