Are there any known asic chips manufactured/produced in China?
Because ASIC's as a general family do far more than just mining - I would assume yes. We are talking things like Digital Signal Processors, network switch fabric chips, usb to serial converters, digital watch/clock and calculator chips, mp3 players, etc. Any circuit or collection of circuits that serves only 1 function can be put into an ASIC. However they would be a pretty big node size and the Chinese Foundries are incapable of making anything competitive even with 28nm mining ASIC's.
https://en.wikipedia.org/wiki/List_of_semiconductor_fabrication_plantsThat list mentions GloFo planning a plant in China but no mention of what node size it would produce. IMHO it would again be for high node size chips that need to be rock-bottom price for consumer electronics. No way in hell would Global Foundries build a bleeding-edge foundry there. No matter what, safe bet that at least for now the new Tariffs put brakes on that plan.