The anomalous <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi>Z</mml:mi><mml:mi>b</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover></mml:math> couplings at the HERA and EIC

To resolve the long-standing discrepancy between precision measurement of bottom quark forward-backward asymmetry at LEP/SLC and Standard Model prediction, we propose a novel method to probe $Zb\bar{b}$ coupling by measuring single-spin $A_e^b$ polarized lepton cross section in neutral current DIS processes with $b$-tagged jet HERA EIC. Depending on tagging efficiency final state $b$-jet, can already partially break degeneracy found anomalous coupling, as implied LEP SLC electroweak data. In first year run EIC, degeneracy, due its much larger luminosity higher electron beam polarization. With enough integrated collected it is possible either verify or exclude data $A_{\rm FB}^b$ puzzle. We also discuss complementary roles proposed EIC $gg \to Zh$ HL-LHC constraining coupling.