To overcome Yb laser, kilowatt-level 1535 nm fiber laser is utilized to in-band pump an Er:Yb co-doped fiber (EYDF) amplifier. An output power of 301 W narrow-linewidth EYDF amplifier operating at 1585 nm, with 3 dB bandwidth of 150 pm and M²<1.4, is experimentally demonstrated. To the best of our knowledge, it is the highest output power in L band narrow-linewidth fiber amplifiers with good beam quality. Theoretically, a new ion transition behavior among energy levels for in-band pumping EYDF is uncovered, and a spatial-mode-resolved nonlinearity-assisted theoretical model is developed to understand its internal dynamics. Numerical simulations reveal that the reduction in optical efficiency is significantly related to excited-state absorption (ESA). ESA has a nonlinear hindering effect on power scaling. It can drastically lower the pump absorption and slope efficiency with increasing pump power for in-band pumped EYDF amplifiers. Meanwhile, to improve power to kilowatt level via in-band pumping, optimized approaches are proposed.