Out of $\underset{\left(I\right)}{H_{2}S{O}_4},\underset{\left(II\right)}{H_2{S}_2{O}_7},\underset{\left(III\right)}{H_{2}S{O}_5}$ and $\underset{\left(IV\right)}{H_2{S}_2{O}_3}$:

The correct option is A. oxidation number of sulphur is $+6$ in all except $IV$

In structures, I, II, and III shown below, the S atom is attached to two oxygen atoms via double bonds and to the other two oxygen atoms via single bonds. Hence, the oxidation number of S in these compounds is +6. In compound IV, the oxidation number of two S atoms is +4.
Thus, statement A is correct.

Peroxy linkage is present in only III. Thus, options B and C are incorrect.

The oxidation number of S in I is +6 and in IV is +4 and 0.
Thus, option D is incorrect.