Peace be upon you. In our mosque, we announce the Adhan according to the Sunnah. We do not follow the unified Adhan system and we have been doing this for a long time now. Some people object to this and call for the adoption of the unified Adhan system which depends on the use of the radio. What is your opinion about this? Do we comply or do we keep following the Sunnah and the righteous predecessors? Does the ruling on the unified Adhan fall under what is called Fiqh Al-Waqi` (Jurisprudence of Contemporary Reality)?

You should follow the practice of the Sunnah. Each mosque announces the Adhan by itself. Do not air the Adhan from the radio, for this is not supported by any evidence. Thus, you have to follow the Sunnah and announce the Adhan yourselves, as this act cannot be done by proxy.
The unified Adhan system does not fall under any category of Fiqh. There is no need for it, since the basic ruling is that every mosque announces the Adhan, following the example of the Prophet (peace be upon him). Scholars agree unanimously on this, without any exceptions.