There are a few stations in India which span different states.
This one came to light recently. Dilwa is on the Gurpa-Gujandih ghat section near Gaya on the Delhi-Kolkata route.
It is nominally in Jharkhand, as mentioned here: https://indiarailinfo.com/station/map/dilwa-dlw/2738
However, you will see this on the platform:
Credits to Debapriya Chakraborty for this discovery.
A couple of other such stations are better known:
Navapur, nominally in Maharashtra on the Surat-Bhusaval section:
However, part of this station lies in Gujarat:
Not sure whether these markings are accurate.
One can make jokes about this bench being partly in a dry zone, enabling alcohol to be consumed only on one side.
Another one which has been round for a long time is Bhawani Mandi, nominally in Rajasthan:
But you will see these signs:
Then there is Hili station in Bangladesh. The boundary commission decided that the railway line itself was to be the border between India and East Pakistan. This becomes apparent here:
Looking from the Indian side. The wall and the rail line are in Bangladesh.
Also see this picture taken from a Bangladeshi train:
Note the cows grazing just within Bangladeshi territory marked by the stone. Clearly they have no problem in crossing the border. Hope they know which side is safer for them.
More weird things happened in the partition of Berlin which became more stringent after the Berlin Wall came up in 1961. While a number of roads and railways were blocked by barriers, there were special cases like Wollank Strasse station on the S-Bahn (which was largely on the surface, unlike the U-Bahn which was largely underground):
This station actually lay in East Berlin. But this platform opened out to a street in West Berlin.
Trains ran through from one side of West Berlin to another, and passengers could board or get down here.
However, no train stopped on the other track-as the Berlin Wall was right next to it. And the East Berliners in the buildings on the right could see the West Berliners going about their lives at this station and beyond.
Bornholmer Strasse station, which featured in various novels and films set in the Cold War, is adjacent to this station: