Is it permissible for a cousin to cut off the shared road leading to my father's house after fifty years of use, claiming that the road passes through his land, knowing that the width of the road does not exceed six meters?

The road is a right for everyone and should be established when needed. No one is permitted to seize a road that people have used for a long time without a known owner. This is indicated by the Hadith: "If you dispute over a road, make it seven cubits." If the road has been used and is wider than seven cubits, no one is permitted to seize any part of it. Therefore, your cousin does not have the right to block the road after his silence for the entire period mentioned. Scholars have also recommended opening a road for a neighbor if they need it.