In this study, an innovative PAN/FCS-NaY TNAM was fabricated using an electrospinning technique for Cu(II) and Pb(II) removal from contaminated water. Top and bottom fibrous layers (M1) were fabricated using a combination of FCS and PAN blends. Middle layer (M2) was electrospun from pure PAN solution and loaded with NaY zeolite particles. The physicochemical properties of the material and fibrous samples were investigated through SEM, FTIR-ATR, DSC, AFM, DMTA analysis, and contact angle measurement. The effective parameters, including initial ions concentration, time, reusability, and pH on the dynamic adsorption performance of the prepared membrane and its stability in the aqueous medium for Cu(II) and Pb(II) ions removal were investigated at a pressure of 0.006 bar. Dynamic metal ions adsorption was modeled using dynamic filtration prediction models such as Thomas and Yoon-Nelson. The fabricated nanostructure fibrous membranes with the removal percentage of Cu(II) and Pb(II) ions (94.6% and 98.7%, respectively) under the optimal operating conditions (initial concentration: 50 ppm, time: 10 min, and pH: 4.6), high compatibility in modeling dynamic filtration (R2 > 0.99), high pure water flux (298 LMH), suitable reusability (four-cycle without significant reduction in adsorption) as well as long-term stability, can be as potential filters in water treatment applications.