Please have a look at the examples in the wiki: [Search for nodes which belong to two different ways][1] and the following one.
one, as well as [Search for street intersections][2]. Can you take it from there to adapt these queries to your specific needs?
[1]: https://wiki.openstreetmap.org/wiki/Overpass_API/Overpass_API_by_Example#Search_for_nodes_which_belong_to_two_different_wayshttps://wiki.openstreetmap.org/wiki/Overpass_API/Overpass_API_by_Example#Search_for_nodes_which_belong_to_two_different_ways
[2]: https://wiki.openstreetmap.org/wiki/Overpass_API/Overpass_API_by_Example#Search_for_street_intersections