Novel intra-boll yield components and Q-score can further evaluate the effect of phosphorus fertilizer on cotton yield and fiber quality

•Boll density was the most sensitive yield trait to extra P supply.•P fertilizer increased boll weight mainly by increasing seeds boll-1 and fibers seed-1.•P fertilizer increased lint percentage via increasing fiber biomass seed-1.•P fertilizer increased fiber length, uniformity and strength, finally promoting Q-score.•Some yield and quality traits of different cultivars responded differently to extra P.