Yes, China is probably developing JASSM now. It's the logical thing to do.I heard rumors Chinese are developing Jassm like a missile and also LRASM. But currently, probably it's not a priority.
There are so many fixed land targets within the 1st Island Chain.
These would be within reach of JASSM launched from the Chinese mainland or from bombers.
And the vast majority of targets would not be covered by ground-based air defence, because the radar/infrared/visual horizon is only 30km.
So stealthy Chinese JASSMs could slip through undetected all the way to their targets, particularly since the skies overhead are going to be contested airspace.
Previously JASSMs weren't worth developing, because China still needed to secure air/maritime superiority over its coastal cities and waters.
But now they are looking firmly at power projection towards the 1st and 2nd Island Chains.
But the rationale for an LRASM version doesn't work as well, because it would need to add expensive guidance systems AND have to head directly towards the SAM systems of a defending warship.
Once the missiles are detected at the radar/infrared/visual horizon, LRASMs are slow, so the defending warship should have enough time to fire multiple defensive SAMs salvoes.
Anyway, back on topic.