physics of ultracold bosonic atoms trapped in optical lattices [@jaksch_98]. The variation of the hopping term, equivalent to kinetic term in continuum models, in the BHM drives a quantum phase transition from the Mott insulator (MI) to the superfluid phase (SF) phase. And this transition has been experimentally observed [@greiner_02]. The inter-particle interaction in the BHM is onsite or contact in nature. The introduction of the nearest neighbour (NN) interaction in the BHM generates two more phases, density wave (DW) and supersolid (SS) phase. This model with the NN interactions is referred to as the extended BHM (eBHM) [@kuhner_00] and shows rich physics compared to the BHM. Such a model captures the physics of dipolar ultracold quantum gases in optical lattices [@baier_16; @bandyopadhyay_19]. A more complex system, ideal to model several condensed matter systems, is to fill the optical lattice with two species Bose-Einstein Condensate (TBEC). A TBEC could be condensate mixture of two different atomic species [@modugno_02; @lercher_11; @mccarron_11; @pasquiou_13; @wacker_15; @wang_16], two hyperfine states of an atom [@myatt_97; @hall_98; @stamper_98; @stenger_98; @maddaloni_00; @delannoy_01; @sadler_06; @mertes_07; @anderson_09; @tojo_10] or two different isotopes of an atomic species [@papp_08; @handel_11; @sugawa_11a]. It was experimentally first realized in the two hyperfine states 