Is a person gets incremented salary in case he had resigned just before the distribution of appraisal letters, but he is working in next financial year for 2 months. My question is that will the person will get incremented salary or he will be paid the old year salary only.

Short and sweet, it depends on the contract of employment, but doubtful.

If a person has been promised a raise, but leaves before the raise takes effect, he doesn't get it. If the raise was to induce him to stay and he does, then he gets it.