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A standard term for this is the noun distinctive. It is used to identify the beliefs or practices that separate one denomination or tradition from another, as opposed to those beliefs that they have in common.
For example, here are several examples of how this is used:
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Words like this depend on the context/perspective you're trying to put forward. If you're trying to be unbiased but indicate the word may fall short of full interprative support, you may consider the word "dogma."
If you're trying to convey sarcasm, contempt, or disdain (not particularly Christian attitudes), then my may consider "conceit" or "heresy."
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Is there a word... that would mean "a unique or controversial interpretation of a specific aspect of Christianity"?
Is there a word? No. Heresy, conceit, dogma, unorthodox teaching, &c. do not imply any kind of uniqueness, as @Lesley's quote from J.L. Packer describes. [I stand corrected. It looks like the noun 'distinctive' is in some use for this idea.]
Is there a phrase? Sure. Christ's visitation of the Americas is a distinctive
or unique doctrine
of the Church of Jesus Christ of Latter Day Saints.
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With regard to a view that does not affect a person’s salvation (for example, that Jesus was a breach birth), it would be acceptable to describe such a view as unorthodox, unique, or singular if no other Christian denomination subscribed to such a view or to simply say they “are of the opinion” that...
However, if a Christian denomination held to a controversial doctrine that denies one or more of the fundamentals of biblical truth, then that belief would be viewed as heretical. For example, a denial of the deity of Christ results in the view that Jesus’s death was insufficient to pay for our sins. A denial of salvation by faith alone results in the teaching that salvation is achieved by our own works. Believing a heretical teaching could prevent a person from coming to saving faith in Christ Jesus.
As unpopular as it might be to brand a teaching as heretical, Jude commended the first Christians to “contend for the faith that was once for all entrusted to the saints”.
J I Packer on heresies: “Since it is beyond the wit of man to invent a new heresy, it is a great help to know the old ones, so that one can spot them when they reappear in modern make-up.”
However, an uncontroversial opinion or interpretation of an insignificant detail of Christian belief would not be a heresy, merely a point of view.