You have applied to the job on 29th January.
Is the present perfect sentence correct though it has specific time.
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This is not the correct use of the present perfect tense as the action has been completed and also the time frame is definite (not continuing into present time or still representing present time). So, you could say this properly by saying "You applied for the job on January 29th" or "You had applied for the job on January 29th."