We study the hybrid bound states in continuum (BIC) in time and spectral domain obtained from Eu3+/Pr3+ doped YPO4 and BiPO4 crystals. The spectral and time domain BIC originates from the interference between broadband fluorescence (FL) and narrowband super-florescence (SP-FWM) due to the dressing effect and crystal phase transition. We present a relationship between BIC and correlation and investigate two-mode and three-mode noise correlation/squeezing when the wavelength of the applied field is fixed at the bright state and dark state. In contrast to the BIC peak, we observe a switch and anti-bunching-like phenomenon at the BIC dip. We realize at the BIC peak point that correlation exhibits multi-oscillations and long coherence time in Pr3+:YPO4 in contrast with Eu3+:YPO4. Further, our two-mode intensity noise correlation experimental results suggest a controllable bandstop filter with an 80% bandwidth contrast and a dual-channel amplifier with an 89% amplitude contrast.