Oh boy. The answer is yes, but the matter of extent is highly contentious. I'm drawing mostly from a lit review I wrote on the subject.

Lloyd Eastman's Abortive Revolution makes the strongest claim, saying that the Blue Shirts, a secret faction within the Kuomintang (KMT, aka Nationalists), took over the KMT. More importantly, he claims Chiang Kai-shek was in on it. Maria Hsia Chang challenged this view, mostly on the grounds that the Blue Shirts weren't truly fascist. Chang and Eastman exchanged multiple articles over this in China Quarterly. My personal view is that it's mostly a result of quibbling; Chang admits that the Blue Shirts were influenced by fascists, but points out that they also admired Stalin and other strong leaders abroad and argues that Chiang himself was not fascist. (There is, incidentally, an argument that the "Blue Shirts" weren't actually fascist but confused with another secret fascist group).

It's worth pointing out that Germany and the Nationalists in China had very good relations, which continued even after Japan, a German ally, went to war with China. Chiang was the superintendent of Whampoa Academy, the Chinese military academy, where several German officers taught. Eastman argues that Max Bauer and Hermann Kriebel, both Germans close to Hitler, exhibited influence through Whampoa, but William Kirby's Germany and Republican China argues that the advisers were kept out of political instruction, and weren't uniformly pro-Nazi. Kirby does point out the Chiang was at least open to the idea, since he learnt fascist theory from Max Bauer's son and sent a secret mission to learn about the Nazi Party, though it's unclear whether he's interested because he sympathizes with their politics or if he wants to use the German military as a model for China's. Personally, I'd say it's a mix of both.

Kirby argues that the fascination with fascism was a byproduct of admiration for Germany. Germany's successful reunification was something many Chinese sought to emulate, and a strong leader was seen as a potential solution to unifying the Nationalists, which were split into several factions. Chinese public discourse often touched on politics abroad as the Chinese looked to restructure their own government. For example, Whampoa Acadamy's journal Whampoa Monthly (黃埔月刊) looked quite favorably upon fascism in several articles and hoped to adapt components, at least, to China, though it's probably also influenced by the Blue Shirts at Whampoa.

TL;DR: Yes, see "Blue Shirts Society", but there is debate over the extent, how involved Chiang Kai-shek was, and whether it really qualifies as full-fledged fascism.