As far as I can see, the only time we played York City in the 50s was in the famous FA Cup Quarter-Final 1-0 defeat in front of the largest crowd ever seen at Meadow Lane.
I’ve come across this game against Sheff Untd on 23rd February 1957 and wonder if this could be the game you were referring to? I remember the game, as we were 2-0 down at half-time and United missed two penalties in the second-half. Russell our centre-half scored both our goals, the second in the 89th minute.
There was a covering of snow on the ground and it was still snowing when the game kicked off. The Notts fans didn’t take kindly to the referee giving the two penalties and amid boos he had to be escorted off at full-time, with some fans throwing snowballs at him!