Step 1: Structure of oxyacids of sulphur.
Different oxyacids of sulphur show different bonding patterns involving sulphur–sulphur and sulphur–oxygen bonds.
Step 2: Analysis of thiosulphuric acid.
Thiosulphuric acid $\mathrm{(H_2S_2O_3)}$ contains one sulphur atom bonded to another sulphur atom through an S=S bond and also contains S=O bonds.
Step 3: Elimination of other options.
Other given oxyacids do not simultaneously contain both S=S and S=O bonds.
Step 4: Conclusion.
Therefore, the correct answer is $\mathrm{H_2S_2O_3$}.