鳍 is usually combined with a modifier: 背鳍 (dorsal fin), 胸鳍 (pectoral fin), 尾鳍 (caudal/tail fin), 鱼鳍 (fish fin in general). The infamous 鱼翅 (yúchì, shark fin) uses a different character.
鱼 is the fish radical and files 鳍 in the aquatic anatomy family - fins, scales, gills are all rendered with 鱼 on the left. Same indexing in 鳞 scale, 鳃 gill, 鲨 shark.
耆 gives the sound qí exactly. The literary 'elder' meaning has no role here - pure phonetic. 耆 itself combines 耂 (old) + 旨 (taste) and shows up rarely in modern Chinese except in compounds like 耆老 (the aged).
