I suppse the intention is for this to be another version of This sentence is false, but it fails.

The sentence

(1) "Is false when preceded by its quotation" is false when preceded by its quotation.

says that the string "Is false when preceded by its quotation" has the property of being false when preceded by its quotation. The sentence is, in fact, that string preceded by its own quotation. However, there is no paradox. The whole sentence (1) can be true, and then the italicised occurrence of the string "Is false when preceded by its quotation" is false. No problem there. Incidentally, it's dubious to ascribe "is false when preceded by its quotation" a truth-value anyway, since it's not a sentence, but merely a verb-phrase.

One could change it to "yields falsehood when predicated of its own quotation". Then you get the sentence "Yields falsehood when predicated of its quotation" yields falsehood when predicated of its quotation, which looks more paradoxical. However, I'm not entirely clear that it really is a paradox, either. There might be some confusion there between predicates and strings that refer to predicates. It depends on how quotation in natural language really works...