Coefficient2[exp, form1, form2, ...] is like Coefficient, but it also allows to extracts coefficients of form1, form2, ... sequentially. To specify the power in formi, write it as {var,pow}.
To keep the prefactor whose coefficient you extracted you need to set the option Prefactor to True.
ex = y0 + ep y1 + a4 (1/ep x1 + x2 + x3 ep) + a4^2 (1/ep^2 z1 + 1/ep z2 + z3 + x4 ep)\text{a4}^2 \left(\frac{\text{z1}}{\text{ep}^2}+\text{ep} \;\text{x4}+\frac{\text{z2}}{\text{ep}}+\text{z3}\right)+\text{a4} \left(\frac{\text{x1}}{\text{ep}}+\text{ep} \;\text{x3}+\text{x2}\right)+\text{ep} \;\text{y1}+\text{y0}
Coefficient2[ex, a4]\frac{\text{x1}}{\text{ep}}+\text{ep} \;\text{x3}+\text{x2}
Coefficient2[ex, a4, 2]\frac{\text{z1}}{\text{ep}^2}+\text{ep} \;\text{x4}+\frac{\text{z2}}{\text{ep}}+\text{z3}
Coefficient2[ex, {a4, 2}]\frac{\text{z1}}{\text{ep}^2}+\text{ep} \;\text{x4}+\frac{\text{z2}}{\text{ep}}+\text{z3}
Coefficient2[ex, {a4, 2}, {ep, -1}]\text{z2}
Coefficient2[ex, {a4, 2}, ep]\text{x4}
Coefficient2[ex, a4, 2, ep]\text{x4}
Coefficient2[ex, {a4, 1}, {ep, 0}]\text{x2}
Coefficient2[ex, a4, ep]\text{x3}
Coefficient2[ex, {a4, 1}, {ep, 0}, Prefactor -> True]\text{a4} \;\text{x2}