Barring The usual of Pedal bearings and bottom bracket- Look at the sprockets. Does it occur in only one chain ring?
Then there are other body related causes as your weight shifts such as a Loose saddle or seat post related problem.
If it is always in the same pedal position it could be any of the above and I doubt it would be Dérailleur or chain related unless the chain is worn and has damage to it throughout the length and as you put power on at that part of the pedal stroke it clicks.
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How long was I in the army? Five foot seven.
Spike Milligan