Pairing enhancement in Betts lattices with next nearest neighbor couplings: Exact results

► We study pairing instabilities in Betts lattices (cells) with reduced size effects. ► Phase separation quantum critical points are found in negative gap region. ► Contour isoline for onset of charge pairing at finite temperatures is calculated. ► Enhancement of pairing is driven by next nearest neighbor coupling. ► Optimized criteria for strong charge pairing instability are formulated.