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I have a set of labells:

      A - no lesion
      B - mild
      C - severe 

If an instance from a class predicted as its nearest class not a big problem compare to an instance predicted as a compeletely different class.

For e.g. if A predicted as B is not a big problem compared to A predicted as C.

Are there any methods to do this? could you please suggest some readings and any public code to do this?

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You need either Ordinal Regression (see also here for R) or Cost-Sensitive Classification. The are a lot of readings and public code examples. Google including the name of your programming language

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