The Trickery Domain Cleric gets access to Invoke Duplicity at 2nd level, which states:
As an action, you create a perfect illusion of yourself that lasts for 1 minute, or until you lose your concentration (as if you were concentrating on a spell). The illusion appears in an unoccupied space that you can see within 30 feet of you. As a bonus action on your turn, you can move the illusion up to 30 feet to a space you can see, but it must remain within 120 feet of you.
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.
Sneak attack states:
Beginning at 1st level, you know how to strike subtly and exploit a foe’s distraction. Once per turn, you can deal an extra 1d6 damage to one creature you hit with an attack [...] if another enemy of the target is within 5 feet of it, that enemy isn’t incapacitated, and you don’t have disadvantage on the attack roll.
It seems pretty clear that the advantage provided to the cleric is exclusive, and that may have an affect on how it interacts with the optional flanking rules (if you're using them), but I'm interested in whether the distraction provided by the illusion is sufficient to be 'subtly exploited' by the rogue's sneak attack - in other words, whether the illusion counts as 'another enemy of the target' for the purposes of this class ability.
This question looks at some of how the illusion works, and this one explores how the inverse is possible (something that is definitely an enemy but not visible to the target can proc Sneak Attack) but it doesn't seem clear to me RAW whether or not this 'perfect illusion' would provide the same support.