The acid in which O-O bonding present is

$H_2S_2O_8$

The correct answer is Option (3) → $H_2S_2O_8$.

The presence of an O-O bond indicates a peroxide linkage. Let's examine each of the options in detail:

1. H₂S₂O₃ (Thiosulfuric acid) 

This acid does not contain an O-O bond. It has sulfur atoms in different oxidation states, but no peroxide linkage.

2. H₂S₂O₆ (Dithionic acid)  

Dithionic acid does not contain an O-O bond. It has sulfur-sulfur bonds but no peroxide linkage.

3. H₂S₂O₈ (Peroxodisulfuric acid) 

This acid contains an O-O bond (peroxide bond) between two oxygen atoms, which connects the two sulfur atoms. This is a key characteristic of peroxodisulfuric acid. The structure includes the S-O-O-S bond.

4. H₂S₄O₆ (Tetrathionic acid)  

Tetrathionic acid does not contain an O-O bond; it has S-S bonds instead.

Conclusion:

The acid containing an O-O bond is H₂S₂O₈ (peroxodisulfuric acid).