Can a trickery cleric's illusory duplicate make opportunity attacks if the cleric has the War Caster feat?

Question

The cleric's Trickery Domain subclass has the Channel Divinity feature "Invoke Duplicity" which creates an illusory duplicate of the cleric and provides the following abilities:

For the duration, you can cast spells as though you were in the illusion’s space, but you must use your own senses. Additionally, when both you and your illusion are within 5 feet of a creature that can see the illusion, you have advantage on attack rolls against that creature, given how distracting the illusion is to the target. [PHB, pg. 63]

Can this duplicate make opportunity attacks? Or, more precisely, can the cleric make opportunity attacks through their duplicate?

If the cleric has the War Caster feat, they are able to use certain spells as opportunity attack "replacements":

When a hostile creature’s movement provokes an opportunity attack from you, you can use your reaction to cast a spell at the creature, rather than making an opportunity attack. The spell must have a casting time of 1 action and must target only that creature. [PHB, pg. 170]

This would be necessary for allowing opportunity attacks via the duplicate because the cleric can only cast spells through them, not make weapon attacks there. (Spells with 1-action or 1-bonus-action casting times cannot normally be used as opportunity attacks, as discussed by Sage Advice here.)

So I think this comes down to a question of reach. Does the illusory duplicate extend the cleric's reach to include the 5 feet around the duplicate because the duplicate allows the cleric to cast spells "as though [they] were in the illusion’s space"? They are allowed to make melee spell attacks within 5 feet of the duplicate, after all. Or is the cleric's reach limited to the 5 feet around them, personally?

Answer 1

No: the duplicate can't even do a normal attack, nor it modifies in any way how you can do an OA.

The duplicate created via Invoke Duplicity can not take any action, reaction or bonus action: in particular, it can not do any attack nor opportunity attack.

Moreover, its presence does not grant the caster any opportunity attack even with the War Caster feat. For example, suppose that a cleric with this feat creates the duplicate 20 feet from them, just next to an Ogre. Then, on their turn, the Ogre moves away from the duplicate: this does not trigger any opportunity attack from any one. Indeed, as previous stated, the duplicate can not do any opportunity attack (OA). Furthermore, the description of the War Caster feat says (emphasis mine):

When a hostile creature’s movement provokes an opportunity attack from you, you can use your reaction to cast a spell at the creature, rather than making an opportunity attack. The spell must have a casting time of 1 action and must target only that creature.

The requirement is that hostile's movement provokes a OA from you, which means that they must move out from your reach. The duplicate does not change your reach: if it were the case, the description would have specified so. An example of an ability that modifies your reach for an opportunity attack is Echo Knight Fighter's Manifest Echo as reported in Thomas' answer; another example that modifies your reach (in general, hence also for opportunity attacks) is the Runic Knight's Runic Juggernaut feature (emphasis mine):

You learn how to amplify your rune-powered transformation. As a result, the extra damage you deal with the Giant’s Might feature increases to 1d10. Moreover, when you use that feature, your size can increase to Huge, and while you are that size, your reach increases by 5 feet.

Answer 2

Invoke Duplicity does not change how opportunity attacks work for you.

Compare to the Echo Knight Fighter's Manifest Echo feature:

When a creature that you can see within 5 feet of your echo moves at least 5 feet away from it, you can use your reaction to make an opportunity attack against that creature as if you were in the echo’s space.

Manifest Echo is quite similar to invoke duplicity, but Manifest Echo explicitly changes how opportunity attacks work for the Echo Knight. Invoke duplicity does not mention reach or opportunity attacks at all, so these things are unchanged for the cleric while the duplicate is active.