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. Inhibited by adenosine 5'-diphosphate (ADP). kcat is 7.8 min(-1). Sulfur metabolism; hydrogen sulfide biosynthesis; sulfite from sulfate. Was identified as a high-confidence drug target (PubMed:19099550, PubMed:19678707, PubMed:25710356). Inhibitors that target the Fe-S cluster have been developed and studied (PubMed:25710356). Belongs to the PAPS reductase family. CysH subfamily.