1.my sister is employed in/on/by/with the railway. What is the correct usage .If all are possible could you tell me the difference.
We can eliminate with straight away. To be employed with something is to share that state of employment with it, i.e. have a coworking relationship. On a technical level, this would mean that the sister and the railway are employed by a common party.
In and on are likewise simple to cast away. They refer to location, which could be correct but since I presume that you seek to convey the message that the sister's employer is the "railway", they don't quite fit.
That just leaves by. It's the right one, because by is what you use when an object or influence does something to something else. "The ball was thrown by Billy," "Dave was shot by Matt," "She stuck by me," all of these are example of by in action. Here, the sister is the party being subjected to a state of employment, and the railway is the entity subjecting her to it. So, in the end, the full sentence should be: my sister is employed by the railway.