The nearest metro station to old Delhi railway station is Chandni Chowk metro station which is at a distance of about 2 km from old Delhi metro station. Chandini Chowk metro station is on the yellow line. 

Shankar Sharma
#1
I live is Delhi so I think I am qualified to answer this Question.
The answer from @kirti agarwal is correct that Chandni Chowk metro station is the nearest metro station to Old Delhi Railway Station but the DISTANCE is not 2 km.
The Old Delhi railway station is just few minutes away from the metro station. All you need to do is just exit from gate number 3 and you will reach the station is just couple of minutes.
Source : https://nearestmetro.info/old-delhi-railway-statio...