Catalyzes the formation of sulfite from adenosine 5'-phosphosulfate (APS) using thioredoxin as an electron donor. [thioredoxin]-disulfide + AMP + 2 H(+) + sulfite = [thioredoxin]-dithiol + adenosine 5'-phosphosulfate Binds 1 [4Fe-4S] cluster per subunit. Km for phosphoadenosine-5'-phosphosulfate (PAPS) is above 100 uM and Vmax is lower than 0.21 pmol/min/mg. Sulfur metabolism; hydrogen sulfide biosynthesis; sulfite from sulfate. Belongs to the PAPS reductase family. CysH subfamily.