Is it permissible to establish Friday Prayer in a new mosque in the village, given that there are two other mosques in it that are not filled with worshippers due to the innovations practiced therein?

The general principle is that it is not permissible to have multiple Friday prayers in a single town, except out of necessity. This necessity could be if the mosque becomes too small for the worshippers, or if it is difficult to reach due to distance, or if there is a fear of discord, and so on.

It is authentically established that during the time of the Prophet, peace and blessings be upon him, there was no mosque in Medina where Friday prayer was held except the Prophet's Mosque. This situation continued during the era of the Rightly Guided Caliphs, may Allah be pleased with them. This indicates the intention to gather Muslims for Friday prayer in a single town under one imam, signaling unity of leadership, bringing hearts together, fostering affection, increasing mutual acquaintance, and emphasizing the meanings of brotherhood.

As long as there are two mosques in your village that are not full of worshippers, are not far apart, and there is no fear of discord, it is not permissible for you to establish Friday prayer in another mosque. This is because it leads to the dispersion of Muslims and contradicts the guidance of the Prophet, peace and blessings be upon him.

The fact that these two mosques contain some innovations does not justify creating another contravention by establishing Friday prayer in a third mosque. Rather, you should advise those in charge of these two mosques and explain to them how their actions contradict the guidance of the Prophet, peace and blessings be upon him. If they do not respond, then the evil of their innovation will revert to them and will not harm you at all. It is permissible to pray Friday prayer behind someone who adheres to innovation.

It should be noted that something is not judged as an innovation unless it is known to be so by people of knowledge.