To whom do the trademark rights contested between Ahmed and Yusuf return, which Yusuf registered in the name of his company before Ahmed, and what is the evidence for that from the Qur'an and Sunnah?

"Whoever is first to something has a greater right to it." A trademark's rights are reserved after its registration, and precedence is given to the priority of registration, not a mere designation. Thus, Yusuf has a greater right to it because he was first to register it.