Are the sentences correct?
Sorry for my judging.
Sorry for my judgment.
If yes, what is there difference.
Sorry for my judgment. If you had failed the person you were judging, and later decided that you hadn't been fair in your judgement, you could conceivably say that.
However, I think that you want to say something different, which is why I asked you for context; both of the above are unlikely but without knowing the context in which you want to use them, it is impossible to correct them.
I wouldn't use "sorry for my judging". It's like saying, "I'm sorry that I judged", and one would need a context for this to make sense. Also, though grammatically correct, it just sounds odd or strange.
The phrase, "sorrry for my judgement" is okay, but as an isolated sentence, it leaves one to wonder why the speaker would say this.
I would use an adjective.
I'm sorry for being so judgemental. - or, I'm sorry for being judgemental. This makes more sense as an isolated sentence, and I can imagine that it would fit more contexts than "sorry for my judgement".
If the person was judging a context, say a boxing match, and kept missing good punches from one boxer, he could say afterwards, "I'm sorry for my judging tonight. I've got the flu, and I'm off my game".