Two types that we know of J20 and FC31 with maybe 2-3 dozen actual aircraft but not enough to call it operational beyond training and demonstration.
Right now.
I.e. it is still more than anyone outside the US.
And good luck to them on such however I expect a less capable fifth gen to result.
Depends on what they are going to try to build.
Speculating, Taiwan needs most of f-35 things:
-dispersion capability(on home ground). Stovl and/or extreme STOL is preferable.
-air superiority mission. Massed dogfights with top-tier opposition to be expected.
-stealth strike(never-ending first day). Because they will
have to go in.
-anti-shipping. Taiwan produces ascms on its own, so it is the simplest part.
-cruise missile intercept. F-16V force with thrir SABRs covers this part just fine, actually.
F-35b - well, there are not that many countries to which f-35 versions are so suitable. But, as we know, it won't happen;
F-35b analogue - well, i doubt they can, even with assistance. Not just anyone can build VTOL(or STOL) fighter, and relaxing this requirement questions the whole endevour;
Another KFX-like 4.5 gen fighter on two F414s.
Supportable(Korea seems to succeed at this point), but what's the point? They need numbers, and KFX-type fighter has obvious limitations. Solves only half of the list of missions from my list. Taiwan just is not Korea.
Producing pure stealthy STOL mudfighter. Like "f-35b analogue", but throwing away all excessives to get a small yet formidable air fighter.
May actually work out, but it's risky(first aircraft of this kind in the world) and even more dependent on us tech assistance.
Forms an opposite to KFX-type, filling another part of the spectrum of missions.