爸

Top radical 父 (father) carries the meaning directly: 爸 is the colloquial reduplicated 'papa' built on the formal 父. The oracle-bone graph of 父 depicts a hand holding a stone axe - the figure of authority who provided. As radical, 父 anchors 爸 firmly in the family-relation sense, distinguishing it from sound-alikes.

Bottom phonetic 巴 supplies the sound - bā matches directly with no shift, just a tone change to bà. 巴 itself depicts a coiled snake or grasping hand. As phonetic in 爸 it gives the babbling 'ba-ba' sound that infants worldwide produce first. Same 巴 phonetic in 把 (bǎ, hold), 吧 (ba, particle), 疤 (bā, scar).