Substitution of La3+ for Ba2+ in LaBaGa3O7 melilite yields a new interstitial-oxide-ion conducting La1+xBa1-x,Ga3O7+0.5x, solid solution, which only extends up to x = 0.35, giving a maximum interstitial oxygen content allowed in La1+xBa1-x,Ga3O7+0.5x as about half of those allowed in La1+xBa1-x,Ga3O7+0.5x. La1.35Ba0.65Ga3O7.175 ceramic displays bulk conductivity similar to 1.9 X 10(-3) S/cm at 600 degrees C, whiCkis lower than those of La-1.35(Sr/Ca)(0.65)Ga3O7.175, showing the reduced mobility for :the oxygen interstitials in La1+xBa1-x,Ga3O7+0.5x than in La1+x(Sr/ Ca)(1-x),Ga3O7+0.5x. Rietveld analysis of neutron powder diffraction data reveals that the oxygen interstitials in La1+xBa1-x,Ga3O7+0.5x are located within the pentagonal tunnels at the Ga level between two La/Ba cations along the c-axis and stabilized via incorporating into the bonding environment of a three-linked GaO4 among the five GaO4 tetrahedra forming the pentagonal tunnels, similar to the Sr and 1.6 Ca counterparts. Both static lattice atomistic simulation and density funtiOnal theory calculation show that LaBaGa3O7 has the largest formation energy for oxygen interstitial defects among La1+xBa1-x,Ga3O7+0.5x (M = Ba, Sr, Ca), consistent with the large Ba2+ cations favoring interstitial oxygen defects in melilite less than the small cations Sr2+ and Ca2+. The cationic-size control of the ability to accommodate the oxygen interstitials and maintain high mobility for the oxygen interstitials in. La1+xBa1-x,Ga3O7+0.5x (M = Ba, Sr, Ca) gallate melilites is understood in terms of local structural relaxation to accommodate and transport the oxygen interstitials. The accommodation and migration of the interstitials in the melilite structure require the tunnel-cations being able to adapt to the synergic size expansion for the interstitial-containing tunnel and contraction for the tunnels neighboring the interstitial-containing tunnel and continuous tunnel-size expansion and contraction. However, the large oxygen bonding separation requirement of the large Ba2+ along the tunnel not only suppresses the ability to accommodate the interstitials in the-tunnels neighboring the Ba2+-containing tunnel but also reduces the mobility of the oxygen interstitials among the pentagonal tunnels.