Answer
$Ag_2CO_3 < BaCO_3 < Na_2CO_3$
Work Step by Step
Na2CO3 is soluble in water
Ksp of BaCO3 $2.58\dot{}10^{-9}$
Ksp of Ag2CO3 $8.46\dot{}10^{-12}$
Increasing solubility: $Ag_2CO_3 < BaCO_3 < Na_2CO_3$
Note: BaCO3 has two ions in solution so $Ksp = s^2$ and Ag2CO3 has three so $Ksp = 4s^3$, but since the Ksp of BaCO3 is higher calculating the solubility directly isn't necessary.