Lemmaphyllum microphyllum C. Presl, Abh. Königl. Böhm. Ges. Wiss., ser. 5 6: 623 1851. (syn: Drymoglossum microphyllum (Presl) C. Chr.; Drymoglossum spatulatum Presl; Lemmaphyllum carnosum var. microphyllum (C.Presl) X.P.Wei; Lemmaphyllum microphyllum var. spathulatum (C. Presl) Nakaike; Lemmaphyllum minimum S. H. Fu; Lemmaphyllum spatulatum C. Presl; Lemmaphyllum squamosum C. Chr.; Taenitis microphylla (C. Presl) Mett. Mett. ex Kuhn);
Arunachal Pradesh to Temp. E. Asia: Assam, China South-Central, China Southeast, East Himalaya, Hainan, Japan, Korea, Nansei-shoto, Taiwan, Vietnam as per POWO (Lepisorus microphyllus (C.Presl) ined.);
China (Anhui, Fujian, Guangdong, Guangxi, Hubei, Jiangxi, Yunnan, Zhejiang), Taiwan, Japan, South Korea, Vietnam, NE-India (Arunachal Pradesh) as per Catalogue of Life;


SK1451 18 Sep 2018 : 8 posts by 4 authors. Attachments (6)- around 700 kb each.

Location: Lantau, Hong Kong 
Date: 14 August 2018
Elevation: 3000 ft.
Habit : Wild 

fern, colloquially called  button fern , i had a basket houseplant about 30 years ago once. but it died in the balcony during a harsh winter. never knew its scientific name. so i was very interested when i saw your case.
your plant is most likely Pyrrosia piloselloides  which is supposed to have stellate hairs on both types of the fronds, sterile round and
fertile oval or longish one you have. but, i cant find the hairs in these pictures, may be they are but i cant see them, thats possible.
my next choice is then  Lemmaphyllum carnosum. this FoC page though
says: i quote: Lemmaphyllum carnosum is superficially very similar to Pyrrosia piloselloides (Linnaeus) M. G. Price. 
The two are separated by the stellate hairs of the Pyrrosia, which are sometimes very sparse. ” end quote
if so, and if there is possibility of even a few hairs
i would go with Pyrrosia pilosellodes whose illustration in FoC page in this link is encouraging
rather than FoC illustration of Lemmaphyllum carnosum  page at this link where fig 1 is Lemmaphyllum carnosum, both sterile and fertile fronds are oblong not round and oblong as in Pyrrosia piloselloides.
but all this discussion is preliminary unless … have seen the case. so we all wait.

Thank you …! Comparing with the net images it looks more closer to Lemmaphyllum microphyllum
however we should wait for … comments. 

that means you did not look at the bw illustrations on foc. the links are given above. please look at them

Ok. Lets follow your way …

Lemmaphyllum carnosum is not reported from HK hence can be discarded.
Lemmaphyllum microphyllum and Pyrrosia adnascens are found in Hong Kong.
I believe this is Lemmaphyllum microphyllum. Pyrrosia leaves are more thinner, Lemmaphyllum has succulent leaves

ok, …, Lemmaphyllum has succulent leaves =  i agree to leaves being succulent looking in the pictures
this is Lemmaphyllum microphyllum