Opportunity attacks are specified as follows (PHB, p. 195):
You can make an opportunity attack when a hostile creature that you can see moves out of your reach.
The Trickery Domain Cleric's Invoke Duplicity feature, on the other hand, creates "a perfect illusion of [the cleric]".
Illusions are not creatures, and therefore, the duplicate does not trigger opportunity attacks.
RAF and potentially RAI, it makes sense.
The duplicate you create is a "perfect illusion of yourself". Therefore, it makes sense that an enemy that doesn't know it's an illusion would try to hit it.
This is probably how I would rule it as the DM*, but do bear in mind that according to RAW, no opportunity attack will be triggered.
*As in: I would rule that anything can trigger an opportunity attack, regardless of whether or not it's a creature. I wouldn't count the duplicate as a creature, that's opening Pandora's Box.
Note that the Invoke Duplicity class feature is poorly defined.
As discussed in this question, we don't really know a lot about the illusion created by Invoke Duplicity. Unlike many illusion spells, it doesn't even say whether or not it's physically tangible (which illusions can be - Shadow Blade, Mirage Arcane or Simulacrum are all proof of that fact). Since other spells that create illusions explicitly mention if things can pass through them, we could conclude that by default, illusions are physically tangible. I would be careful about that, though - it makes checking for traps trivial by using physically tangible illusions.