Engineered Kondo screening and nonzero Berry phase in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>SrTiO</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>LaTiO</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>SrTiO</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> heterostructures

Controlling the interplay between localized spins and itinerant electrons at the oxide interfaces can lead to exotic magnetic states. Here we devise ${\mathrm{SrTiO}}_{3}/{\mathrm{LaTiO}}_{3}/{\mathrm{SrTiO}}_{3}$ heterostructures with varied thickness of the ${\mathrm{LaTiO}}_{3}$ layer ($n$ monolayers) to investigate the magnetic interactions in the two-dimensional electron gas system. The heterostructures exhibit significant Kondo effect when the ${\mathrm{LaTiO}}_{3}$ layer is rather thin $(n =2,10)$, manifesting the strong interaction between the itinerant electrons and the localized magnetic moments at the interfaces, while the Kondo effect is greatly inhibited when $n =20$. Notably, distinct Shubnikov--de Haas oscillations are observed and a nonzero Berry phase of \ensuremath{\pi} is extracted when the ${\mathrm{LaTiO}}_{3}$ layer is rather thin $(n =2,10)$, which is absent in the heterostructure with thicker ${\mathrm{LaTiO}}_{3}$ layer $(n =20)$. The observed phenomena are consistently interpreted as a result of subband splitting and symmetry breaking due to the interplay between the interfacial Rashba spin-orbit coupling and the magnetic orderings in the heterostructures. Our findings provide a route for exploring and manipulating nontrivial electronic band structures at complex oxide interfaces.