Step 1: Recall the meaning of disproportionation.
A disproportionation reaction occurs when the same element in a compound gets oxidized and reduced at the same time.
So, we need to check whether the same element shows two different changes in oxidation number.
Step 2: Check option (1).
In
\[
\mathrm{Hg_2Cl_2 \longrightarrow Hg+HgCl_2}
\]
Mercury in \(\mathrm{Hg_2Cl_2}\) has average oxidation state \(+1\).
It changes to
\[
0
\]
in \(\mathrm{Hg}\) and
\[
+2
\]
in \(\mathrm{HgCl_2}\).
So, it is a disproportionation reaction.
Step 3: Check option (2).
In
\[
\mathrm{4H_3PO_3 \longrightarrow 3H_3PO_4+PH_3}
\]
Phosphorus in \(\mathrm{H_3PO_3}\) is \(+3\).
It changes to \(+5\) in \(\mathrm{H_3PO_4}\) and \(-3\) in \(\mathrm{PH_3}\).
So, it is a disproportionation reaction.
Step 4: Check option (3).
In
\[
\mathrm{Cl_2+2NaOH \longrightarrow NaCl+NaOCl+H_2O}
\]
Chlorine changes from
\[
0
\]
to
\[
-1
\]
in \(\mathrm{NaCl}\) and
\[
+1
\]
in \(\mathrm{NaOCl}\).
So, it is a disproportionation reaction.
Step 5: Check option (4).
In
\[
\mathrm{BaO_2+H_2SO_4 \longrightarrow BaSO_4+H_2O_2}
\]
Oxygen in peroxide remains in the oxidation state
\[
-1
\]
There is no simultaneous oxidation and reduction of the same element.
Hence, this is not a disproportionation reaction.
Step 6: Final conclusion.
Therefore, the reaction which is not a disproportionation reaction is
\[
\boxed{\mathrm{BaO_2+H_2SO_4 \longrightarrow BaSO_4+H_2O_2}}
\]