We present the properties of the ground state and low-energy excitations of Bose-Hubbard chains with a geometry that varies from open to closed and with a tunable twisted link. In the vicinity of the symmetric π-flux case the system behaves as an interacting gas of discrete semifluxons for finite chains and interactions in the Josephson regime. The energy spectrum of the system is studied by direct diagonalization and by solving the corresponding Bogoliubov-de Gennes equations. The atom-atom interactions are found to enhance the presence of strongly correlated macroscopic superpositions of semifluxons.