帕

Left cloth radical (Kangxi #50) - the indexing radical and the meaning anchor. A 帕 (handkerchief) is by definition a small piece of cloth, so 巾 directly supplies the semantics. Same cloth-family: 布 cloth, 帽 hat, 帘 curtain, 帐 canopy, 带 belt - all things made of fabric.

Right side 白 supplies the sound - bái → pà, drifting through an Old Chinese b/p alternation that pairs many 白-phonetic chars in voiced/voiceless sets. A faint semantic hint too: handkerchiefs are stereotypically white. Same phonetic series: 拍 (clap), 怕 (fear), 伯 (uncle), 泊 (moor), 珀 (amber).